the pitch of a softball into the air, free to experience only gravity as it moves, the strike of the bat and the return of the ball to gravity's embrace, the leap of the basketball player into the air in anticipation of dunking the ball. This is a kind of poetry written in the air by gravity, the satisfaction of launching a football into the hands of gravity to have it delivered exactly to the place where it needed to be. All of these are examples of projectile motion here written out in a kind of concocted perfection as the ball is launched from a moving cart and the ball returns to the cart because the horizontal component of its motion is not affected by the fact that it has been granted a vertical component of motion. Let us explore this kind of motion and all of the benefits and mathematical beauty that it reveals in nature. Let's begin to look more deeply at projectile motion and build a toolkit based on our previous explorations of motion in more than one dimension to describe this motion. First, let's lay out some of the key ideas that we're going to cover in this lecture. First of all, we will find that projectile motion is a special kind of motion that happens when motion in one dimension is unaffected by motion in any other dimension. The motion of airborne objects near the surface of the earth is an excellent example of projectile motion. We can describe that kind of motion using the ideas we have already developed. And in cases of projectile motion where there is constant acceleration along only one of the coordinate directions, the observed trajectory in space will be a parabola. These are the ideas that we will develop more fully in this lecture. Now, there are, as you've seen, many common examples of projectile motion that we experience every day. Consider the cartoon over on the right which show silhouetted figures in various games of sports involving catching, throwing, or deflecting a ball. A ball flying through the air, moving only under the force of gravity, or a person, after pushing off the ground in a jumping maneuver, now unable to contact any other surface to exert any other forces and thus subjected only to gravity. These are examples of projectile motion that are very common in everyday life. Let's consider a very specific situation which will illustrate all the features that we need to explore in projectile motion. Consider the situation that is depicted on the right hand side of this slide. We have some kind of projectile launching device. In this case it's a tube that can allow air to force a projectile out of one end of the tube. This is a blowgun or an air gun and it has been aimed so that the barrel points straight at this metal can which is hanging here from a stand. When the ball leaves the barrel of the gun, the can is simultaneously dropped from the stand. Both the can and the steel ball are now executing projectile motion. The question that we would like to explore is will the steel ball hit the can or will it miss the can? We can analyze the situations, for instance, such as firing a steel ball with an initial velocity and dropping a can from rest simultaneously using the equations of motion that we have been playing with and developing so far and try to answer this question. But before we do that in a mathematical sense, let's take a look experimentally at what would be required to set up exactly the situation that I have just described. The essence of this demonstration are three pieces. One is a metal tube that is capable of holding a small ball bearing. This metal ball bearing is like a bullet that one can load into the barrel of the tube in the front here. The tube is connected at the back to a hose that goes to a supply of air that's provided in the classroom workbench environment. So I'm able to turn the handle on the air nozzle and get it to force air through the tube and push on the ball bearing, eventually shoving it out of the end of the tube. So we can already see that there is a force that's present to accelerate and launch the ball, and that is the force of the air pushing on the ball inside the tube. But once the ball exits the tube, the air is really no longer acting on it. That force was only present to accelerate the ball inside the tube, and it diminishes quite rapidly once the ball leaves the tube. So out here, there is no air pressure pushing from one direction only on the ball, and so we would expect that there would be no forces acting on the ball. But of course, that's not true. There is a force that will act on the ball. It's acting on the ball constantly throughout this, and it really begins to take over once the ball exits the tube, and that is gravity. Gravity will tend to want to accelerate the ball down at a rate of about 9.8 meters per second squared. So once the ball exits the tube, we can think of at least one force that's definitely acting all the time on this ball, and that is gravity, and it should be exerting a force in the downward direction, yielding an acceleration of 9.8 meters per second squared. Now this ball is made of metal, and as a result of that, it has some inertia that prevents it from falling prey easily to small forces that would tend to accelerate it. Now as we know in the real world, there's air, and if we wave our hands around, we can feel the resistance of air. And in fact, air resistance is a force that always tends to sap motion out of an object because it always resists the motion of an object in its direction of motion against that direction. So certainly, air resistance will be acting on this ball, but it turns out to be a relatively minor force compared to gravity, and so we will neglect it in this particular experiment. Let's look at some of the other elements of this. Over here, I have a small electromagnet. This is a device that only produces a magnetic field when an electric current is run through the device. And if you look closely here, you'll see that there is a white pair of wires that goes up and into the electromagnet. Now I can power it using this device over here, which is a power supply. It's simply connected into the wall, and it converts the voltage from the wall into something that's a bit more friendly for this electromagnet. And so with a flick of the dial here and a gentle turn, I can start running a current through this by exerting a voltage of about six volts on the wire. So now that I have a voltage, and thus the potential for a current inside of this device, there should be a magnetic field. And I can verify this by switching off the power supply and showing you that I'm unable to get this metal can to stick to the electromagnet. On the other hand, if I switch on the voltage, and now I attempt to stick the can to the magnet, bingo! It easily remains there in place, neither moving up nor down nor left nor right, nor forward nor backward. There are no net forces acting on this can, and it is now in an equilibrium state. It cannot move at all. So let's think about what we've done. We have a device that can accelerate a small metal projectile, a small metal ball bearing. That projectile conveniently is aimed when it leaves this barrel at the can. I took the effort to line up the barrel of this to point, like a little rifle, at the can. Now here's the last ingredient in this exercise, and that is that the current that's powering that electromagnet is controlled by a little switch right here. The current is on, the metal can is clearly attached to the electromagnet. But if I push the switch and I break the electric circuit, I interrupt the flow of current to the electromagnet, and what happens? Well, an electromagnet is only magnetic when there's a current flowing through there. If I interrupt the electric current, there will be no magnetic field. Without the counterbalancing magnetic force from the electromagnet, gravity is now free to act solely and only on this can, pulling it closer to the center of the earth. So here's our experiment. Now that we've had a chance to see how such an experiment could be conducted, let's begin to analyze this using the principles of motion and physics that we have developed so far. We should begin by describing the situation using a coordinate system with an x and a y-axis, and I have denoted the units of distance along each of those axes to be meters. We're going to use this to represent and describe the steel ball, the can, and the features of the motion. We can then place a mark in the coordinate system, indicating the initial location of the steel ball, the moment that it exits the blowgun, and is no longer being acted upon by the compressed air inside the tube. And we mark this location using a blue dot shown over here on the left in the graph. Note that I have placed the blue dot at one meter above the horizontal, and along the horizontal axis, it actually sits at zero meters. This point one indicates the leftmost extent of the x-axis here. This location under the blue dot is actually zero meters in the coordinate system. Let us then also mark the initial location of the can just at the moment that it is released from the stand that it is dropped. Remember, the exiting of the steel ball from the gun and the dropping of the can occur simultaneously, and the moment in time that we will state where those events both occur is t0, t equals zero seconds. That's our initial time for the motions to begin. We mark the location of the can with a red dot. Please note that I have placed the can at a height of three meters above the floor, and two meters from where the steel ball exits the gun. And as we are going to see, the motion of the steel ball will look like the black path, the curve that I've now drawn here, shown in the graph. Before we begin to actually explore the motion where this path emerges from in a mathematical sense, let us explore key points of the motion, accepting this curve as the correct mathematical description, before we dive into the details I just mentioned. There are a few key and interesting points along the motion curve of the steel ball projectile. The blue dot already marks one of them. It's the initial location of the steel ball in x and y. We can denote that location x0 comma y0. It is here that the steel ball leaves the blowgun with an initial velocity, and I have represented the arrow of that velocity vector, and written it out mathematically here. It has a horizontal component. It has a vertical component. And one of the key features of this velocity is that the barrel of the gun, and thus the steel ball when it exits the barrel, are initially aimed at where the can begins its motion. So where the can is hanging from the stand in the experiment. So note that the ball begins at 0 comma 1 meters. The can is at 2 comma 3 meters. And so if we turn off gravity for a moment, if we want the steel ball to hit the can, its velocity vector has to point along a line that executes equal motion in the x direction as in the y direction in the same amount of time. So after some amount of time, we want the steel ball to be here if there's no gravity. Thus the can can't fall. It just sits where it's parked when we initially fire the ball. And then in the next unit of time, we want the steel ball to traverse this distance continuing along the diagonal between these grid points to strike the can. The initial velocity of the ball must be aimed directly at the can, even though gravity will act on both of these objects once they are released from either the stand in the case of the can, or from the tube in the case of the steel ball. So we will need a velocity vector in this depiction of the situation whose horizontal component is the same as its vertical component, regardless of what the total magnitude of the velocity is. We just, based on this picture, need the components to be equal. Now in a different situation where the coordinates of the can are not what I've shown here, we might need a different kind of breakdown of the components of velocity. And these are things that we can explore in homework and in class. So this is one interesting point in the motion, the initial location of the steel ball with its initial velocity v0. The apex of the motion, that is, the highest point along the motion curve in y, that the steel ball manages to reach, is another interesting key point in the motion. Since gravity accelerates the steel ball downward toward the surface of the earth, there will come a point where the ball no longer moves up or down its vertical motion appears to pause for a moment. And then after that point it reverses its vertical motion and begins to fall from rest at the top of the motion curve. At this point the ball is only moving horizontally. There are no forces acting along the horizontal direction. The ball continues to move horizontally the whole time, but its vertical motion is more complex because at first it's going against the direction of acceleration due to gravity, but eventually gravity wins and it reverses the direction vertically of motion of the ball. The horizontal component, however, is independent from the vertical component. This will allow us to analyze this motion. This purple arrow indicates the velocity of the ball, which only has a horizontal component at the apex of the motion. As you can see, the motion has two halves before the apex and after the apex. Before the apex, the combination of horizontal and vertical motion for the steel ball points up and to the right, but after the apex the combination of horizontal and vertical motion points down and to the right. And this combination is ultimately what produces this curve, whose actual mathematical shape is a parabola. Let's begin to analyze the motion of the steel ball and consider what's happening, but for now only in the horizontal direction. The initial velocity in the horizontal direction is given by the x component of the velocity v0x and it points in the i hat direction in the positive x direction and this I have written here as a unit vector indicating just the direction of the horizontal component along x. Because there is no source of acceleration in the horizontal direction, the steel ball has left the blowgun. It's no longer being pushed on by the air inside the gun. There is no force acting horizontally if we neglect air resistance and we are doing that in this problem as an aside for a small steel ball. Neglecting air resistance is a reasonable assumption. It has a fairly aerodynamic shape. It's also heavy and not so subject to the whims of air resistance as it moves through the air. So we can approximate that there is no source of acceleration or deceleration in the horizontal direction and so after it exits the blowgun and the blowgun can no longer act on the steel ball, there is no force that can speed up or slow down the component of velocity in the x direction. Remember the equation of motion, that the velocity at a later time is equal to the velocity at an earlier time plus the acceleration along that direction times the time. But since the component of the acceleration in the x direction is zero, we see that only in the horizontal direction the velocity remains constant throughout the entire motion and in fact at every point in the motion until an external force acts on the ball, for instance the steel ball strikes the floor and the carpet and the floor change what the ball is doing the horizontal velocity will always be the same. So we actually now have an equation of motion that gives the x coordinate at any time t after the steel ball is fired from the barrel of the blowgun and again to remind you it begins its journey at 0 comma 1 meters and the can begins its journey, although we're not talking about the can right now at 2 comma 3 meters and here is the equation of motion for the steel ball in the x direction. This will tell you the x coordinate of the steel ball at any time t after being launched from x0 with a velocity v0x. So this isn't so bad, it's nice not to have acceleration in one of the directions, it makes the equation fairly simple. Now let's consider what's happening in the vertical direction. The initial velocity in the vertical direction has a magnitude v0y and it points originally in the positive y direction. The steel ball is moving to the right and up initially, it's being fired upward toward the can. So its initial velocity is to the right and up and so it must be that the vertical component of its overall velocity vector points upward with some initial length v0y at time 0 and that's denoted by the blue arrow in the graph. Now gravity of course is acting in the vertical direction, it exerts a constant downward acceleration of 9.8 meters per second squared in magnitude and thus the acceleration component in the y direction is negative g where g is 9.81 meters per second squared. This will cause the vertical velocity to change with time. Again remember the equation of motion relating velocity acceleration and time, the velocity at any time t is given by the initial velocity plus the acceleration times time but in the vertical direction the acceleration is negative g times time. So we have this equation which tells us that the velocity will while first being positive eventually be overtaken by the acceleration due to gravity reversed and point downward more and more and more as gravity accelerates the ball downward toward the floor. Now after the apex and remember that the apex is where the vertical velocity is exactly zero meters per second in the vertical direction the steel ball is neither moving upward nor downward at the apex. After that point acceleration reverses the direction of velocity and the velocity vector points down and its magnitude will grow larger and larger as gravity continues to act on the ball. So we can write an equation of motion that gives the y-coordinate at any time t and that's shown here. The y-coordinate at any time t will be its initial y-coordinate plus its initial velocity in the y-direction times time minus one-half gt squared and the minus sign is because the acceleration is in the negative direction so a in the y-direction is replaced by negative g. So let us now write the two equations one for the horizontal location and one for the vertical location at any time t. I've written those out here on the slide and I've now indicated here this expected trajectory for the motion and we'll see again where this arises from the moment although we already have a kind of qualitative understanding of why this motion should be curved as the horizontal component moves with constant velocity and no acceleration whereas the vertical component has a changing velocity due to the constant acceleration due to gravity. Now these are the equations that tell us position in space given velocity and acceleration and we can similarly write the components of the velocity itself at any time t and again we have a horizontal component that is constant with all time because no acceleration acts on the horizontal component or neglecting air resistance. In the vertical direction however the velocity components magnitude does change with time and in fact at at some point given the acceleration it will reverse and point downward. Now using the equations on the previous slide we can return to the original question that motivated all of this mathematical and physical activity. Will the steel ball so fired strike the can? To hit the can the steel ball must reach the same coordinates as the can at the same moment in time t. Now we know what the x coordinate of the can will be at any time t because the can is dropped from rest. It's not moving to the left it's not moving to the right when it's dropped and so its x coordinate is the same throughout all of its motion. x sub can and we'll use the subscript can to denote quantities for the can is the same as x zero can the initial position of the can along the x axis. So we can ask a question at what time does the steel ball reach an x value of x sub can? Again taking a look at this picture the x location of the can is two meters from where the steel ball started which is considered to be zero meters along the x axis. So we can actually use algebra to answer the question. We have an equation of motion for the x coordinate of the steel ball at any time t after it's launched. We know that we want to find out at what time t x becomes x sub can which is two meters. So we plug in x sub can set that equal to the initial position of the steel ball plus v zero x times t. Well we know all of these quantities except the time. We know x can it's two meters. We know x zero for the steel ball it's zero meters. We know v zero x for the steel ball it's three meters per second which was written on a previous slide. We're assuming that the steel ball is fired with an x initial velocity of three meters per second and a y component of velocity that's also three meters per second in the upward direction. So v zero x is three meters per second and if we plug all these numbers in and rearrange and solve for time we find out that the time at which the steel ball reaches an x coordinate of two meters along the x axis which is where the can is is two thirds of a second or point six six six dot dot dot seconds after the steel ball is launched. Now using that time we can take the t value of two-thirds of a second and we can plug it back into the equation for the y coordinate and find out what the y coordinate of the steel ball will be when it reaches that x coordinate. And we find when we do this and I encourage you to try this yourself go back a slide get those equations of motion for x and y v zero x v zero y g and t. We now know the time from the x equation we can substitute that into the y equation and solve for the y coordinate at t equals two-thirds seconds when x equals x can two meters. And when we do that we found out that the y coordinate is point eight two meters when t equals two-thirds of a second. So we know where the steel ball is supposed to be when it reaches the x coordinate of the can. It will be at a height of point eight two meters at two-thirds of a second after its initial launch. So let's think about the can. Where will the can be at t equals two-thirds of a second? Well the can is merely being dropped at the very same moment that the steel ball leaves the blowgun. We call that time t zero and in our problem that's zero seconds. At first as gravity begins to act with constant acceleration on the can its initial velocity is zero. It has no velocity in the x direction. It has no velocity in the y direction. But as gravity continues to act with constant acceleration on the can and since gravity is the only force that acts on the can the can begins to accelerate straight down along the vertical axis toward the ground and that acceleration in the y direction is negative g there is no acceleration in the x direction so there will never be any velocity in the x direction. Now this is the same constant acceleration that the steel ball is experiencing. The can's velocity continues to increase more and more but it only ever has a vertical component since no forces act in the horizontal direction and there was no initial velocity imparted by any force to the can when it was released in that direction. The position and velocity of the can are then given by these equations of motion. The horizontal position of the can is the same at any time t. It's always x zero can which is two meters. The y position of the can however is a bit more complicated. It is the initial position in y of the can which is three meters above the ground plus the initial velocity of the can times t well the initial velocity is zero it starts from rest so in fact this term goes away because zero times t is zero and then we have to add to that one half a t squared well the acceleration is negative g so we have negative one half g t squared and by throwing out this middle term because it's zero we can simplify this equation to y zero can minus one half g t squared and the velocity of the can is given only by a y term there is no x term because it has no velocity in the x direction to begin with there are no accelerating forces in the x direction so there is never any x component of the velocity there's only a y component of the velocity and it's given by v zero y can minus g t because the can is accelerated down from rest and in fact since v zero y can is zero this is just negative g t in the j hat direction. So will the steel ball hit the can in other words after t equals two-thirds of a second so two-thirds of a second after the can is dropped where will the can be in height well we know where it will be in the horizontal direction it will be exactly where it started it will be at two meters what will its y coordinate be well it started at three meters and if we plug in two-thirds of a second and solve given its initial height the acceleration and the time which is two-thirds of a second we find that the y coordinate the height of the can above the ground after two-thirds of a second is point eight two meters and if this looks familiar there's a reason why the steel balls coordinates that t equals two-thirds of a second are x equals two meters and y equals point eight two meters and the cans coordinates at the same time two-thirds of a second are also two meters and point eight two meters in the x and y directions respectively. So we conclude that the steel ball hits the can but how can this be if we think about the initial situations of the steel ball being fired upward toward the can and the can being dropped from rest it seems amazing that in fact the ball hits the can but the reason for this is because the steel ball was initially aimed at where the can started and after they both enter projectile motion they both experience the same constant acceleration and so projectile motion is extremely powerful it is motivated simply by the fact that we have independent motion in these two directions x and y we could easily extend this to a third direction z if we wanted to and in the special case of objects in projectile motion near the surface of the earth we have this constant downward acceleration from gravity and so we find that we have these situations where we can not only describe very well the motion using the mathematics we've already developed but for this specific situation where a projectile is aimed at a target and the target and the projectile both enter projectile motion in the gravitational field of the earth with no other forces acting on them at the same time that in fact they meet at some point in space later it's really remarkable now there are many examples of projectile motion in the universe a basketball free throw where you carefully aim and then throw a basketball up above a hoop in the hopes of getting it to come down and enter the hoop and make a basket throwing any ball in fact into the air in such a way the the ball will observe projectile motion once it leaves your hand because it will have no forces again neglecting air resistance it will have no forces acting in a direction perpendicular to gravity so along the horizontal and it will feel only the constant acceleration due to gravity in the vertical direction another example is jumping while moving if you are running and then jump into the air you now no longer have any surfaces to touch you can't change your motion and you will be in projectile motion in the gravitational field of the earth so think about track and field long jumping things like that jumping over hurdles those kinds of events involve ideally projectile motion where the body makes no contact with another surface until the motion is completed archery riflery any activity where an object is launched into the air and cannot provide its own acceleration rockets don't count rockets carry fuel the fuel is burned this exerts a force on the rocket and so this can affect its motion but any projectile that has no way of exerting a force say by using chemical energy or some other form of energy to convert that into a into motion these will experience projectile motion so think about just how useful it can be to know that when you meet the conditions required for projectile motion it is extremely predictable that motion can be extremely well described now i'm not going to show you the punchline to the steel ball and can demonstration in here we're going to do that in class but you will see that if you set the situation up correctly as i said aiming with steel ball at the can having them release as shown in the experiment earlier at the same time that in fact the steel ball will hit the can now the caveat on all of this is of course there's this thing called the real world and in the real world things are more complex than what i've laid out here you had better account for things for instance like air resistance and also when you fire a projectile off the surface of the earth and it's no longer making contact with the surface of the earth and because we live on a planet that's rotating we go through one day night cycle every 24 hours that motion of the earth the ground moving and the air resistance this adds real complexity to the problem of course in real situations in artillery calculations in thinking about designing something like a baseball stadium at various altitudes or where air atmospheric conditions are slightly different than they would be say at sea level or in another park you need to take these things into account when you're thinking about how many home runs might get hit where the artillery shell might land and so forth but over short distances with appropriately aerodynamic projectiles at low altitudes with weak air resistance all of this works remarkably well and these conditions while they sound very limiting and and yes they do take you away from the most realistic calculations they are nonetheless good enough assumptions that you can make a lot of progress with this subject let's talk about the path of projectile motion i said earlier that the path is a parabola and in fact i'm going to reinforce that and show you that now so again the path of a projectile in this kind of motion with a constant acceleration in one direction no acceleration in the other it has this common shape the parabola now the details of the parabola its height its width these things can vary based on the initial conditions of the situation how fast you fire the projectile how strongly acceleration is and so forth but in general this shape will be preserved assuming you can neglect things like air resistance and so forth the equation for a parabola whose apex or as is shown over here on the right whose minimum point is located at some point in space and i've denoted that x apex and y apex and with a focus a distance f from the apex so the apex would be here and the the focus might be somewhere up here again review the definitions of parabolas that you might have learned in high school for instance to refresh your memory of all of this stuff the equation for a parabola with these conditions is as follows the y coordinate of the parabola is given by one over four times the focus distance times the quantity x minus x apex all squared plus y apex so this allows you to define a parabola that's offset from the origin and raised above the origin for instance with because it has this apex location that isn't zero comma zero but if we set the apex to be zero comma zero we recover a much simpler and perhaps more familiar equation for the parabola that you would have seen in high school y equals a constant times x squared and that constant is one over four times the focus this is another way of representing a parabola this equation over here is perfectly valid it's a slightly more general form of this equation with the focus and other pieces like the displacement from the origin and the x-axis and the height above the x-axis that the parabola starts etc that's that's shown over here on the right in this equation these are all equations for parabolas of various kinds generalized or otherwise what about motion well if we take the equations for x and y those coordinates for the steel ball at any time t after it's fired and if we rearrange them so that we can solve for t from one of them and plug that equation for time into the second equation we then find this eliminating time from these equations we only have y x x not y not v zero x v zero y and g and what do we see well we have the the height of the parabola above its initial starting point or below its apex is given by a term that is linear in x multiplied by the y component of velocity and that looks very similar to the b term over here in the parabola equation and another term that is quadratic in x and that looks very similar to the a term over here in the equation so we see in fact that the relationship between the y coordinate of the steel ball and the x coordinate of the steel ball at any time t after it's launched is given by a parabolic equation so this is just the equation for a parabola in a slightly expanded form over the generic equation specific to our projectile motion situation so again neglecting things like air resistance the rotation of the earth under the projectile etc the motion of a projectile under these conditions is completely predictable before we close out the lecture let's play around a little bit with projectile motion in a computer-based simulation a sort of game-like environment i have here a cannon that's capable of firing various projectiles and you can see that it's initially set to fire at an angle of 80 degrees above the horizontal there's a target that i'm supposed to hit by shooting projectiles out of the cannon i'm going to move the target over to about 20 meters from where the cannon is located so right about here so i can start by firing a projectile from the cannon i've selected pumpkins with a mass of five kilograms a diameter of just a little over a third of a meter i'm going to fire them from the cannon and watch as they execute projectile motion and see if i can hit the target so let's fire a pumpkin here goes a pumpkin up into the air and we see that it leaves a beautiful parabolic trajectory as simulated by the computer in the air the pumpkin smashes here on the ground we are far from our target we clearly missed the target but i can adjust the firing angle of this let me try firing a little lower maybe 56 degrees and fire well that was terrible this clearly overshot the target but you can see again we have this parabolic arc albeit wider the pumpkin flies further along the horizontal direction although it doesn't go as high in the vertical direction because of the firing angle of the pumpkin and the effects of gravity during the motion it's clear i need to split the difference and do something in between here so let's try something more like 65 degrees and fire the pumpkin one more time ah so close but again you can see that i've increased the firing angle relative to the ground of the pumpkin and so the pumpkin goes a little bit higher but not as far as it did before and you can begin to see these trade-offs in the motion of the pumpkin in projectile motion if i aim the pumpkin higher into the air when i fire it indeed it will go high up into the air but it won't go as far horizontally if i aim too low it'll go far horizontally but it won't go as high as that otherwise would and so hitting the target is a careful balancing act of firing up into the air and firing too low let's try one more firing angle let's try 68 degrees and see what happens so now i fire so close let's try one more time we'll try 70 degrees you can try this game on your own these simulators are available aha i got into the outer ring of the target not too bad these simulations are available from a group called vet vet.colorado.edu i'll make sure to put a link in the slides around the course website and we can probably improve our game a little bit more by maybe switching this to 72 degrees and firing let's see if we can get dead center on the target not too bad clearly the magic number here is going to be 71 and if i fire one more time indeed boom i'm in the sweet spot of the target so this will give you a little opportunity to play around with projectile motion without hurting anybody or yourself and you can try various projectiles you can also do things like turning on air resistance so as a last test of this let's try air resistance we're going to add resistance due to air now so the pumpkin is going to feel a drag force as it moves through the air i'm going to fire at the same angle 71 degrees let's watch what happens oh indeed we see that adding in a bit more realistic aspect that is resistance to motion from air greatly alters the trajectory of the pumpkin it still looks parabolic but it's not a perfect parabola anymore and in fact we fall short of the target because our motion is being resisted by the air through which the pumpkin is moving so feel free to play around with this this is an excellent way to get some intuition and a game like environment for physics and it will give you a more hands-on feel for projectile motion when you can neglect air resistance and think about trying to hit a target by balancing how much horizontal velocity and how much vertical velocity you present in the presence of gravity let's review the key ideas that we have been exposed to in this lecture on projectile motion we've seen that projectile motion is a special kind of motion that happens when motion in one dimension is unaffected by motion in any other dimension the motion of airborne objects near the surface of the earth is a really excellent example of projectile motion think back to the beginning of the video with the basketball player jumping into the air to dunk the ball or the pitch of a softball toward the batter or the throwing of a football to aim at some distant target make that shot as best you can these are all examples of projectile motion gravity gives us an outstanding laboratory near the surface of the earth to explore this kind of motion and we have seen that we can describe such motion using ideas that we have already developed regarding position and time and velocity and constant acceleration in cases of projectile motion where there is a constant acceleration along only one of the coordinate directions we have seen that the observed trajectory of motion in space will be a parabola we have seen how to make approximations for instance the removal of air resistance from consideration removal of the rotation of the earth underneath a projectile that's been launched from the surface of the earth and we've seen that for certain limiting cases and assumptions it's it's not a bad thing to do we do need to be cautious in the real world these forces can play major roles especially over large distances or with projectiles that are not very aerodynamic projectile motion is seen to be a beautiful kind of motion a predictable kind of motion one that we can not only describe with the mathematical tools that we have developed so far but whose outcomes we can predict quite reliably as long as we have made a valid set of assumptions


Well hello my friends and welcome back to my channel. Today I'm going to be doing my monthly view for April 2019 if we want to look back together. This is my March and I will leave the video that I did on this in a card for you guys. What I am using is the Aaron Condren 2019 monthly planner. These are the petite planners and yeah it's called a petite monthly planner and I've just been really liking this more than my like Aaron Condren life planner full layout in the monthly view for some reason. I just think that this is easier, something to grab. I don't know I just I just really really like it. So anyway there are a few things already in here because I forgot that I was going to be filming these videos but yeah so there's a couple things in here on Tuesday the second I worked from home because my dad's car that stays here in the winter needed like a front windshield auto glass repaired and then on Wednesday I went to Sam's Club. So let's get this party started. Okay this is it. This is my April. I hope you guys enjoyed the video. If you did make sure to give it a thumbs up and I will be back sharing May which this is what I have for May so far. So I have like a wild which is why my mom's coming into town. She's going to be watching Doyle for the long weekend and then she's going to stay for a few extra days too and yeah so that is it. I will link all the sources for the stickers and things that I can find down below and if you have any questions feel free to leave them in the comments and I will see y'all in the next video. Bye guys. Well folks it's time to kick it old school.


Hey, buddy, we'll see how it is. I don't think it's anything that's going to be too, too serious. Couldn't finish the game. So we'll see where things are tomorrow. Yeah, different. Yeah, something different here. Well, I think that when we did, we didn't finish. There were some mistakes.  We knew when we practiced about moving hop around on third down and just disappointing that we aren't set and then being able to move one of our better players around to help us get a conversion. So, you know, it's a penalty there. We're not set. You know, we have the touchdown, the full return. Can't protect the quarterback. And then, you know, just not scoring down there inside the red zone.  There'll probably be some better plays once we have a chance to look at it, you know. But then it's just not complimentary enough.  So it's hard to play any game when you're not complimenting each other and there's these mistakes. We're talking about the little things that get to be done shift at this stage of the season, you're disappointed you're still getting stuff like 12 men in the field running and through the kicker. Yeah, always disappointed. You know, I mean, we've become our own version of Friday Tape.  You know, we have to all be tuned in and some of those things that you can overcome and we're not where we need to be to be able to overcome those things. And I know Caleb, you know, was really, you know, trying to take that role of special teams and, you know, he had driven the wing into the punter last week and that's legal.   Talked about his violence and, but then you just have to know where you're now you're on a different unit. And that, you know, I guess trying to finish can't override the decision-making. You know, it's a young player that, you know, again, we've been searching for outside linebackers to help us in a special teams game and Caleb's starting to do that.  Well, there's good, there's bad.    It's, you know, it's hard when you leave a lot of guys in against zone coverage.  So, you know, I think that there's always a balance and we've talked about some of the things that we need to be able to do when you can run the football and you can then, you know, run some play passes that have, you know, different blocking schemes, different angles, you know, that's where you can kind of leave guys in because, you know, you get some cell from the underneath coverage and then you're able to hit some things behind it or take a shot. So, you know, you have to be able to do some of those things to keep players in. And third down, you know, probably got to chip once in a while but also got to try to get some guys out to help the quarterback. Yeah, I mean, we have to be able to protect our quarterback. I mean, the numbers are the numbers, you know. So you got to be able to protect the quarterback if you want to be able to throw the football in this league. I don't know. We didn't make the play. So I don't know what the reaction would have been. I think that's a hypothetical question but you have to, you know, go out there and be able to make some of those plays.  Same thing on defense. We have to be able to knock the ball out of somebody's hand. We're going to be able to hit it off the quarterback, tip it up in the air. Yeah, that's pro football. And they're frustrated that you need to be win with so far in the division. Well, you know, just being able to run it in, being able to, you know, protect the quarterback and, you know, just didn't happen. You know, we were giving them credit but weren't able to score. It's a huge play. I'm not sure. I'm really not, you know, I don't have any answers for knee injuries on gunner play. I know that that's something that the league has looked at that's a so long play with guys tugging on you. So that was one of the injuries that occurred today. Well, we'll go by a case-by-case basis later on. You know, just quarterback, when the quarterback gets hit, nothing good's going to happen from it. He was probably, question, he was less than a hundred percent. He got himself in a position to play. Yeah, I mean, everybody's trying, I think, to get themselves in a position to play. Cavo and SMB will and, you know, will wants to play for us. He does and, you know, we got to do a better job and, you know, protect whoever's back there throwing a football and get open quicker and, you know, execute our offense. You know, be at all to run and marry some things up off that and then keep it in third and manageable. We'll do everybody else. I guess dealing with another one of these, how tough is it for some of you to get some lemon down here? I mean, I don't, it's the same thing. I don't know, same. We'll talk the same, say the same thing. We just didn't play well enough today, to win.  You know, man, never big plays created touchdowns. You know, it gets a little bit more going for us. We weren't able to do that today. I don't think it is a great job controlling the game. Do you feel limited in what you can do as soon as it's coming off the front right now? Well, just ain't played well enough. Brian said he feels like John Wick at the end of his own hard to watch the four of us get beat up to the degree not down to the games and their feeling like that. Yeah, I'm not going to keep my teammates down. We all done played well enough as a group. You know, it's tough to see you before they get hit, but we always got to be better collectively to be able to make plays and not have sex. Are you surprised that after all those weeks of saying you have to be better collectively, that hasn't happened? Sit again? Are you surprised that after all these weeks of saying that you guys need to be better collectively, you're still signed up? I just said earlier, it's the same old thing. We'll say the same old thing. It's all I can say. You know, it just hasn't been the year we want to just be. Got one more game, try to finish strong with that one. How do you approach that last game, Derrick, given the results of it? Go back to work, paying some energy, just work hard throughout the week, paying intensity. Everybody try to make each other better. And if we do that, we can try to go in. How much would it mean to get that one and not go winless? I mean, it would definitely put a smile on everybody's faces that they don't mind. To go out with a win, it was going to be tough. Another vision opponent, they're a great team, but got to figure it out somehow. The Andre goes over 1,000 yards. You go over 1,000 a day. That a little bit of a payoff for the work you put in and still be able to do that as this day of your career? I don't know, really. Stats of stats, us not playing as well as we need to be able to win games is more important. If you do what you're supposed to do, then other stats and everything else take care of yourself.   Next gap coming in, I guess full-back to the exact amount. What's the first version level, like, as a team, though, having a good one? Yeah, that's hard.  If it's blocking, then blocking. If it's catching, catching, throwing, throwing, whatever the case may be, we just got to do a better job of doing our jobs. So you're just there where you've got no chance? Yeah, definitely. Did you see Will or what was he doing? Yeah, I talked to Will. He gave me a brief thing. I guess we'll find out more in the next couple of days. But yeah, I feel for him. Obviously, he's battling kind of a freak thing, just the way it happened. But I guess we'll see what would happen. How much does a team just kind of mix in the spark, early in games, or maybe change their momentum, or just get some energy going? Yeah, you just got to do a better job of executing. You can't go out and go through and out and expect the energy to be really high. Find a way to execute early in games and score points. Back in here. Oh, man, it's always good being in Houston. Love the fans, love the city. You still got a lot of love for these good folks here. What do you want to do when you go to the town? Of course, going over the town. It means a lot to me. No matter what the record says, you got to have a little pride and take accountability and what you can do and what you can control. And I feel like that's my mindset. Plus, it's flat. I don't know, man. Football, they get paid too. Does it feel limited at a certain point when there's so much pressure and it's harder to have plays develop downfields? That's a question that is above my pay grade. The only thing I can do is go control what I can when the ball is thrown to me. It's always frustrating to lose for me. I'm a competitor.   So it's always frustrating to lose. Just having faith in, knowing life is short, man. How big has your faith been in something like that? My faith has been big since I came out the loan in section A projects.


Does this look familiar? It's what appears on your oscilloscope when your probe is left ungrounded, though it may look a bit different depending on where you live. That spiky AC component has a frequency of 60 Hz, the same frequency used by main supply voltage here in the US. Yep, this 140 millivolt peak-to-peak signal is being generated by my wall power here. Without a reference to circuit ground, the scope's probe will pick up noise generated by nearby power sources. So consider seeing this signal a reminder to please connect your ground clip. Much better.


Well, to discuss this so-called absolute need for austerity measures as the British Chancellor coins it, is the Executive Director of Positive Money, Fran Beut, who works with banks and the UK government to campaign for a democratic and sustainable money system. Thank you for coming in. Now, surely Osborne is completely reversing what he said before the Brexit vote, when he was predicting doom and gloom, and now he says the economy is fundamentally stable. I think that millions of people that voted to leave the UK did so as a response to this very unequal society that we live in in the UK. I think there are the 20 constituencies where there were the strongest vote leave, the strongest number of people that voted to leave. The median income is something like £18,000. So it would be the worst response for Osborne now to increase taxes and cut spending on the poorest people, kind of confirming that actually the government doesn't really care about their future. But I also think it would be equally dangerous for Osborne to allow other policies that increase inequality to be pursued, such as monetary policy, including the Bank of England. So one policy that they've been pursuing is quantitative easing, which is where central banks create money and flood financial markets with it. And I think that increased the wealth of the top 5% by about £128,000. And exactly these kind of policies that have been leading to the frustrations that people have in this increasing inequality and that have resulted in the UK voting to leave the EU. But the fact that the pound has gone down, I mean, is that bad or good news? I mean, it's obviously bad news for holiday makers, but it might be good news for exporters. I think that fundamentally the pound going down is a sign of volatility in the UK and the economic instability of the kind of coming in the short term and the medium term. We already have a trade deficit, so we're very reliant on imports and it's going to increase the cost of those, which will have an impact on the cost of living. And I think what Osborne needs to be worried about is this volatility turning into potentially a recession. And what a lot of economists are saying is that the UK needs an economic stimulus, which is the opposite of spending cuts and increase in taxes. So, one of the ways that economists are proposing that we have an economic stimulus is potentially through monetary policy, through actually the Bank of England creating money, but rather than flooding financial markets with it, getting it into the real economy into people's pockets. And that's something that positive money advocates for. We call it public money creation. But that's kind of Keynesianism or neo-Keynesianism, and it's not the philosophy of the Conservative Party in Britain, is it? They believe in a very different policy. Yeah, but yeah, I mean, absolutely, it's a new idea, so the kind of public money creation. But I think that even the chair of the Federal Reserve, Janet Yellen, less than two weeks ago, actually suggested that we need to be considering these kind of ideas and have them in monetary policy toolkits. And I think that Osborne needs to realise that what the economic instability, since the referendum is exposed, is that we have an economy that is skewed towards property and financial markets. We rely on these oversized banks and housing bubbles. And actually, this is a real wake-up call that he needs to be thinking about new ways of re-balancing the economy, so that it works for people and not just for banks and property speculators. Well, Osborne, of course, is a kind of lame duck, as is David Cameron. Soon we will have a new Prime Minister, a new Chancellor. We don't know who they're going to be. Do you think those two people, whoever they are, should now work in a very different way from Cameron and Osborne have been doing over the last six years? Well, hopefully, I mean, as I said, I think this is a real, it's a kind of unfortunate wake-up call, because it's come about in quite an abrupt and a sudden way, this economic instability. But it is a real wake-up call that the future political leadership need to take on, that we can't go on in this way of just having an economy based on an oversized financial sector and housing bubbles. We need to rebalance the economy. And in the short-term and medium-term, all options need to be on the table, including ideas such as public money creation, which have been promoted by economists and gaining further traction. But what sort of policies do you now advocate in the near term as Britain negotiates its Brexit? What should it be trying to get from the European Union? Well, I think, you know, in terms of stabilising the economy, the kind of the key thing is that a decision is made, an agreement with the EU is made, whether that is to, you know, trigger Article 50 straight away and how we actually leave the EU, those decisions really need to be made as soon as possible in order to kind of stable markets, but also investors and businesses in the UK. If we're going to see a devaluing of the pound, we're going to see potentially increasing the cost of imports. So that's an opportunity for businesses in the UK to actually fill the gap there. But if there's a lot of economic uncertainty, then potentially they won't be the investment. Should Britain try and stay in the single market as much as possible and therefore make concessions on the freedom of movement issue, which is so sacrosanct? I think that it's obviously not a straightforward issue, but I think the key is that we want to rebalance the economy towards one that's a lot that's not just focused on big banks and property yet. And I think that ideally, from an economic perspective, we could have stayed within the single market and actually moved away slowly from having, being so reliant on the banking sector and the financial sector and property markets. But that hasn't happened. So we're having to, well, they're having to negotiate quite quickly our exit conditions. And I think that what we should be concerned about is that under the kind of crisis situation and very much lack of political leadership, that we don't allow lobbyists from the finance sector or from vested interests to be shaping the demands that are on the table. We need to think about why people voted to leave, which is essentially because they don't see a future for themselves, they don't see themselves being considered in government economic policy, and they see increasing inequality. And if we're going to really address those concerns, then we need fundamental change of the money banking system and the economy.


History as a race between state power and social power. Just as the two basic and mutually exclusive interrelations between men are peaceful cooperation or coercive exploitation, production or predation, so the history of mankind, particularly its economic history, may be considered as a contest between these two principles. On the one hand there is creative productivity, peaceful exchange and cooperation. On the other, coercive dictation and predation over those social relations. Albert J. Nock happily termed these contesting forces social power and state power. Social power is man's power over nature, his cooperative transformation of nature's resources and insight into nature's laws for the benefit of all participating individuals. Social power is the power over nature, the living standards achieved by men in mutual exchange. State power, as we have seen, is the coercive and parasitic seizure of this production, a draining of the fruits of society for the benefit of non-productive, actually anti-productive, rulers. While social power is over nature, state power is power over man. Through history, man's productive and creative forces have, time and again, carved out new ways of transforming nature for man's benefit. These have been the times when social power has spurted ahead of state power and when the degree of state encroachment over society has considerably lessened. But always, after a greater or smaller time lag, the state has moved into these new areas to cripple and confiscate social power once more. If the 17th through 19th centuries were, in many countries of the West, times of accelerating social power and a corollary increase in freedom, peace and material welfare, the 20th century has been primarily an age in which state power has been catching up, with a consequent reversion to slavery, war and destruction. In this century, the human race faces once again the virulent reign of the state, of the state now armed with the fruits of man's creative powers, confiscated and perverted to its own aims. The last few centuries were times when men tried to place constitutional and other limits on the state, only to find that such limits, as with all other attempts, have failed. Of all the numerous forms that governments have taken over the centuries, of all the concepts and institutions that have been tried, none has succeeded in keeping the state in check. The problem of the state is evidently as far from solution as ever. Perhaps new paths of inquiry must be explored if the successful final solution of the state question is ever to be attained.


So I actually ordered a bunch of ceramics from YesStyle and some other Decor for my house and I'm waiting for that to arrive, but you know how I've been living off of plastic plates Yeah, well that was getting hard and I couldn't eat my favorite egg rice So I stopped by Taizai yesterday and picked up a few plates and bowls.  Maybe for wine nights I just got home from radio and I just wanted to sit down and turn on the camera because today is a very meaningful day for me and it's because I got my First-ever paycheck after living in Korea Yeah, I know that sounds crazy, but it's my first time ever like working hard and Getting paid for it and you might be like how is that possible, but I did make money as ladies code But none of it was physically mine because it all went to the company to pay off our debt So for the past seven years like I didn't know what it felt like to like make my own money and Today I got my first-ever paycheck for the past month from working. I don't know why I'm getting so emotional Not planning on crying like this So I got my first paycheck from radio for the past month of working there independently and Just seeing that amount Which isn't even like a lot If you guys are probably thinking like I got paid so much or something It's not but it's just meaningful to me because it's like my hard-earned money Kind of like drives me to work harder now and it's something that I enjoy doing So getting paid for something that you enjoy is also very special So in Korea, they have this tradition of like buying your parents their book or like long John's red long John's with your first paycheck and But you know people don't really wear long John's anymore, and it's not that cold so I am planning to send my parents some allowance with this first paycheck and that's been something that I've been wanting to do for so long and Finally at age 28 with my first paycheck I can do that Of course, it's not gonna be much, but I know things are tough over there with The coronavirus and all the businesses shutting down and stuff. So I just want to help with Whatever I can and just to be able to do that I think it's something that I've dreamt of doing for so long. I hope I'm not sounding like I'm bragging, but I'm just so Overwhelmed that I can do this and I honestly didn't even know it was gonna be today I just knew that was gonna be the end of the month or the beginning very beginning of the next month But I went into radio today, and they were all like oh like it was payday today So I went in and checked and just saw that I got paid. All right It's time to wash up now. I think I'll be able to sleep very well today We just got a gun for that page I'ma tell me when they I'll be famous Remember when she I always wanted to try this compression pack. I think that's what it's called You know you put your large clothing like your large jackets and coats in there and it compresses it into a really thin plastic bag so I bought some from Taizou to try it out and I've put two of my coats in here since I Feel like it's spring now. It's officially spring.  Let's try Getting ready for radio for 20 p.m I just had some lunch and I watched an episode of Anne with Annie Just doing a quick Makeup look.   I thought it would fade back into blonde, but It's taking a while for that the back of my hair though. It is fading a lot quicker than Everywhere else for some reason the blue is basically all gone My cramps were really bad this morning. So I did some stretches eyebrows are super dark. So I always Use an eyebrow mascara to kind of make it lighter.  This is from Joa It's like a k-beauty brand based in New York and my mom gave it to me when I was in New York this past January I've been using this blush for like the past three years Really love it.  I do have to kind of Think about how I'm gonna look that day a little bit because if it was just like radio with my voice I wouldn't care as much but because we are live daily on the YouTube channel I do have to do my makeup and look Decent every single day, but yeah on days when I feel lazy I do like just wear a hat so I can kind of cover my face, but most of the times I try to look Decent My lips are a bit chapped right now, so I'm just gonna put some lip balm on and I'll be putting a lip color when I'm about to leave a little later This is my makeup look for today. Nothing much just blush eyebrows Lips bronzer This is a lazy makeup look so I got another package and this is something that I Got myself as a gift for you know being independent and moving out and living on my own ever since I could remember like since I was in like junior high school I've always wanted a record player and I told myself when I you know have a house of my own I'm going to buy myself one and I finally did It came all the way from America But the shipping was very quick. I got myself a stereo turntable system from Crossley and mine is to switch to It comes with Speakers as well. It looks like this right now. This is where the LP goes and these are the two speakers. Oh It's beautiful. It's gonna take me some time to learn how to use this I'm gonna leave it there for now, but I think I'm going to get a separate like coffee table for the Record player. I can connect my phone to that as well and use the Bluetooth since this product is from the states The plug is a little bit different. So I had to get an adapter and I'm currently waiting for that right now Because I can't just use any adapters or else it might break. I love the white with the light wooden color This feels so nice You can't wait to set this up and listen to some music with it I only have three LPs right now. I have a lot more at home back in New York So I might ask my mom to send me those the next time she gets the chance to When I get it set up, I will show you guys Please stay tuned. I'm about to make myself some lunch and my menu today is this it's from Don't Spikes brand and I got it as a gift. I received like 10 packs of these and I finished everything except this last one This is really tasty and easy to make All you have to do is put it on the frying pan It's marinated very sweet. So I like it. It kind of looks like a patty I'm gonna make sure the fire is on low My rice is being cooked in there So you cook this for three to five minutes on each side with low heat and that's it I finally put together the turntable last night. Totally forgot to film it It was in such a rush after I got home from radio and just started putting it together and Surprisingly, I did it. I feel like I'm getting better and better at you know Putting things together. It's really big. It's a lot bigger than I expected so I put it in the corner right here and I didn't really look up the reviews for this because I found it on a Korean site and There were some Korean reviews on it, which were all good and I just decided to order it because I really fell in love with the design and It was affordable. I've been listening to it last night and this morning I have to say I'm really satisfied with overall quality. I Did buy it for 225,000 which is like $220 which I know is a bit more expensive than how much it is in America, but I mean considering the shipping and the tax and everything I'm Not complaining. I have the honne LP in there right now I only have three LP's right now Billy Joel's 52nd straight Totally vintage. I also have this Jolly Christmas Frank Sinatra Which is great to listen to even when it's not Christmas and then the CD that's in there is honnes Yeah, so basically the sound quality I think it's Superb for The price that I got it for and since it's just my first turntable I didn't want to invest too much money into it and You know, hopefully when I move to a bigger and nicer place, I can get an even nicer one I am totally satisfied. I would recommend it I just can't wait to get more LP so I can enjoy and take advantage of this turntable to the fullest One thing that bothers me though is this This is too big. This is what it originally came with and this is the adapter that I needed to buy I'm going to need to figure out a way to hide this and it's so heavy too. So That is one of the cons But I'll figure out a way still waiting for more furniture to come so my background is Doesn't look so messy, but please bear with me So one thing I realized after I moved in here was You know how I didn't want to live in an office tell because it was too tiny And it wouldn't have enough room for me to fit all my stuff in because office tells are usually just One rooms like just a studio just go in and it's like a huge box studio, right? But I realized because those office tells are a lot smaller They have a lot of storage space whether it's like in the ceilings on the sides They have built-in closets and built-in drawers and stuff like that, but this house has nothing has no drawers It has no storage space except for the Semi veranda looking thing next to the closet space, which I got rid of to make it into like a bigger room So besides that there's literally no storage space except in the kitchen, but that's really tiny I've just been needing to buy boxes to hide a lot of my Stuff I should have taken that into consideration But besides that I'm having a ball and I'm really enjoying myself Living alone here about that to chill for the living room and that needs a lot more work As well and get rid of the things some things that don't belong up there so I want to say thank you to everyone who's been showing me so much support and Love for the adulting series It really drives me to you know Update weekly for you guys because I know you guys are waiting for it and you guys are looking forward to another episode Thank you everyone for the sweet comments. You guys leave me. It really means a lot to me and gives me a lot of strength and Makes me feel like I'm not in this alone So thank you guys and I hope you guys will continue to enjoy the adulting series and I'll see you guys in the next video Stay safe everyone. Bye. Bye


Hey, this is Brett and this 2022 Ram 3500 Limited Longhorn Crew Cab Longbox Dually, level one is stock number 13861ZA. I am here at Summit Automotive in Fond du Lac, Wisconsin, you're new and used heavy duty truck and Ram headquarters, this 2022 Ram 3500 has the 6.7 liter high output Cummins diesel engine 420 horsepower 1075 foot pounds of torque it's paired up with the ice and heavy duty six speed automatic transmission and this truck has been fully safety and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off per the state of Wisconsin inspection process and this truck is 100% ready to go this one can tow up to 32,600 pounds and has a max payload of 5,182 pounds found those on Ram's tow guide website I will link that in the description below I'm gonna go all the way around in this video inside underneath started up take a look under the hood show about show you all the options and just give you the most accurate representation that I can of the truck diamond black crystal pearls of color I shoot all my videos in 4k if you like the videos consider subscribing to the YouTube channel click the bell notifications and get updates on the videos I do each and every day as well as having access to one of the largest catalogs of vehicle and heavy-duty truck walk-rounds on YouTube 9,000 videos and counting this one comes with the really nice 17 inch polished aluminum wheels and it has nexon rhodium HTX tires these are LT 235 80 R 17s and they have right around half the tread left in the front here frame and underbodies exceptionally clean on this truck this is a one owner clean title history clean car facts out of North Dakota front fenders in excellent condition you get those fender flares on there with that limited package LED headlamps LED running lights and LED fog lamps I'm gonna turn all those on at the end of the video so you can see just how great they are front bumpers in excellent shape you get the front bumper parking sensors on there it also comes with a Western heavy-duty grill guard that's in really nice shape as well and the hood is in really nice condition I didn't see any dense or dings on there get the cab lights up top passenger side front fender is absolutely perfect passenger side front wheel no major scuffs or scrapes on there and check out this paint diamond black crystal pearl one of my favorite colors on the Rams or any vehicle for that matter you get a lot of yellow or gold flake in it purples and blues really pops in the sunlight you can see just how nice that paint is as you go down this side of this 2000 and 22 ram 3500 take note of how clean the body is how reflective and mirror like that paint is once again I take these HD videos so if you're far away or even if you're close by and you just cannot make the trip down but you're still interested in purchasing the vehicle you can see the truck hear the truck and of confidence in the vehicle that you're looking at before you even get here so when you do get here there's absolutely no surprises and you can make a smart and informed buying decision from wherever you're at if this video helps you make that buying decision let your salesmen know that you saw the video that I was helpful and that Brett sent you very nice down that side no dense no dings does have the power running boards it does have the 3m tape which is keeping your dually tub looking good back wheels are in excellent condition as well no scuffs or scrapes or corrosion back tires have just about as much tread as the front tires and the frame and underbody is in fantastic condition remember one owner from North Dakota has all the remaining factory exhaust very little to no corrosion lower rockers all look really good and it does have the power running boards I always like showing both sides that you know that both sides are working nicely there they go dually tub looks really good I didn't see any dents I didn't see any dings on there I didn't see any scuffs or scrapes or scratches coming down the back here rear bumper looks great no dense or dings and that does have the backup parking sensors the full towing package which includes a receiver hitch seven pin wiring and then this is your hookup for your trailer backup assist the tailgate is in very nice condition as well it is a power drop down tailgate with the shock down assist so it's now we're going to slam on you this one comes with a spraying bedliner a goose neck hitch seven pin wiring you also get a hundred fifteen volt four hundred watt plug in LED bed lights that you can turn on and off back here and there's your seven pin wiring for the bed that spraying bedliner goes on to the tailgate which is a very nice feature to have as well shuts nice and solidly you do get the LED tail lamps as well coming down the driver side just as clean as that passenger side no major dents or dings on the box do we tub looks pretty good and for full disclosure this back wheel just as nice as the rest looks really good down the rest of the side of the truck the doors and cab are all in fantastic condition look how reflective that paint is this one has the heated fold-up tow mirrors they have blind spot monitoring built-in directional signals this one does have the 360 camera on it as well and LED side lights I'll turn those on at the end of the video these mirrors do power fold in like so and see the power running boards on the driver side working just as well as that passenger side these back seats are heated on the outboard side latch child safety system for any child car seats you may want to put back here power sign rear window with the built-in rear defrost you get the longhorn limited patch the nice design on there as well these seats fold up and there is a load floor which is nice if you got muddy boots or tools put them on there you're not going to get your seats dirty or if you have pets put both sides down and they got a nice flat place to lay and they won't get your seats dirty and then you get storage under here looks like it has a winter front and a receiver hitch reducer you get the limited longhorn all-weather floor mats back here as well two USBs two USB C's 115 volt 400 watt plug-in and the heated seat buttons get these kind of imitation saddlebags on the back here these carpet squares come out of the all-weather format for winter get the nice woodgrain trim on the doors and child safety locks on the back doors as well inside and bottoms of the doors all look really good show you the vins sticker here no previously owned in Canada trucks here there's a tire and loading information sticker inside the limited longhorn package gives you the tan and brown leather bucket seats in the front no rips no tears on these you get the same patches on the backrest and the seats are in really nice condition there same design on there both these seats are heated and cooled you get the all-weather floor mats up front here as well auto headlamps power pedals power windows locks mirrors leather bolster woodgrain trim these mirrors do power fold in like I was saying I like showing both sides so you know that both sides are working properly you also get the memory driver seat and power blind spot mirrors so check out that outside mirror you can control that on either side which is really nice for the passenger side then you get this kind of bronze trim on the door handles and around the doors looks really good hop inside check out the miles the radio and everything that this truck has to offer on the interior you get the seven inch LCD display with the limited longhorn animation at the beginning digital speedometer compass display battery voltage oil temperature and you can change all those corners to read whatever you want this instrument cluster is special for the limited longhorn package as well you can see with kind of the goldish bronze trim on there as well and then you get the special leather wrapped and woodgrain trim steering wheel cruise controls on the right gear selector on the right Bluetooth and information center controls on the left you get that woodgrain trim on the bottom as well and audio controls in the back of the steering wheel there's your shifter for that six speed ison heavy duty transmission this one has the uconnect five 12 inch radio this one is supposed to be five times faster than the uconnect four system there is highway 41 so you can see that the navigation system is working properly you get AM FM and Sirius XM radio capabilities as well as Bluetooth and USB hookups and Alexa you get your climate controls on here including the dual climate controls and you can control all these things on the screen or you can control them on the side of the screen right there so one does have stability control the Harman Kardon premium sound system a 12 volt power point up there as well and then you have all your different apps on here I'm not going to go through all of these but it does have off-road pages which are pretty cool and then we'll check out the cameras here so you have your surround view camera which you can see right there the grill guard gets in the way of that your backup camera they made these cameras HD so it's easy to get hooked up to your bow camper trailer first time every time you got a wide view of the back a wide view of the front a narrow view of the front which once again that grill guard is hampering you get the cargo cam so you can see what's going on in the back of the truck and then you get the normal backup cam you can zoom in on the receiver hitch to get hooked up to your bow camper trailer first time every time and then you these are my favorite cameras on the whole truck you can zoom in on the side this is backing up so if you're backing up a trailer or a camper can you imagine how great that would be I wish my truck had those cameras and then you can hook up an auxiliary camera as well and that's pretty much it everything on the radio like I said we could go through all the different apps on there but that would take forever push button four-wheel drive factory brake controller factory exhaust brake tow haul mode front and rear parking sensors you can turn those off and on you get a wireless cell phone charge pad two usb's two usb season and aux jack and you get your cupholders right here keyless entry with remote start and power drop down tailgate you also get I believe coin holders right there you also get the limited longhorn edition badge on that center council that's all leather wrapped dual glove box glove boxes you get the longhorn kind of burned into that wood there and the passenger side format and seat are in fantastic conditions still has the old tager on it you get the speakers in the ceiling part of that Harman Kardon premium sound system map lights assistant sos buttons power drop down tailgate and your power sliding rear window button auto dimmy mirror and your home link buttons for your garage door security systems and lighting systems if I forgot anything let me know in the comments below let's start it up take a look at those lights and take a look under the hood starts right up no check engine lights or anything like that there we go I would personally like to thank you for checking out the video today and hopefully from this hd video you've been able to verify the quality condition options and of course cleanliness of this truck all the way around inside now you can see all those lights are working very nicely as are the cab lights under the hood we have the 6.7 liter high output Cummins diesel engine 420 horsepower 1075 foot-pounds of torque engine bay is very clean runs very smooth and once again this truck has been fully safe and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off there is the emissions sticker and this truck is 100% ready to go I would highly recommend it from a quality and condition standpoint I didn't see one single dent or ding on it and to see more pictures of this truck or one of other 550 new news cars trucks scvs minivans wranglers half tons three quarter tons one tons you name it we got to go to the website right there summitauto.com full pictures and descriptions of every single vehicle all at summitauto.com if you want to check out more hd videos you can go to youtube.com slash summitauto click the bell notifications get updates on the videos I do each and every day as well as having access to one of the largest catalogs of vehicle and heavy-duty truck walk-arounds on youtube 9,000 videos in county in fact in a second we'll see a link to subscribe to my youtube channel in the upper left a link to all the ram 3500 truck videos I've ever done in the upper right a link to this vehicle on our website in the lower left and a link to one of our latest youtube videos in the lower right click those check us out we're super excited to help you with this ultra clean 2022 ram 3500 crew cab long box dual rear wheel limited longhorn level one in diamond black crystal pearl thank you so much for checking out the video remember to like subscribe and share on the youtube channel i really appreciate it thanks again