This is Think Tech Hawaii. Community matters here. Okay, we're back. We're live. We're here on Energy in America here on Think Tech. And on a Wednesday afternoon in the three o'clock block with Lou Pruirisi, he's the CEO of E-Princk and Energy Policy Think Tank in Washington, D.C., and he's taking time off for a conference to join us, and we really appreciate that. Lou, thank you very much. Happy to be here, Jay. So it was very interesting this week. We heard that the administration was repealing some regulations adopted during the Obama period, pushing the, what do you call it, CAFE standards from 30 miles per gallon to 50 miles a gallon. And now that's been repealed and they're reconsidering the 50 miles. They may find something else, but we won't know what that is for some time. And it offers all kinds of questions and issues and possibilities and I'm so glad that we can talk about it with you now. So tell us what happened. Okay, so I think it's very important to talk about what the reality of the corporate average fuel economy is and how the regulatory program fits in with that. So if you think about this program going back to the, oh, as far back as the Arab oil embargo in the mid-70s, the motivation for improving fuel efficiency came out of a sense that we were importing too much oil, which we used to make gasoline, that we were reliant on insecure and expensive sources of foreign oil, and that we should have a program not only, maybe you can recall this. If you remember in the 70s, nobody could drive more than 55 miles an hour. Oh, sure. Yeah, we had reduced the amount of time people could drive, how fast they could drive. Then we said, well, you know, we need to make our cars more fuel efficient. And economists always say, well, just put a big tax on them. That'll do it. You know what they do in Europe. We don't like to do things that way. We like to have a kind of sub-mandate. So we have this corporate average fuel economy. But it's very important to remember that its original intent was based on this concern over not necessarily environment, but on our reliance on foreign oil. Yes. Now, at the same time, at the same time, going back to the 60s, the government also began to control what comes out of the tailpipe of an automobile. And if you go back to the 50s and 60s, all kinds of stuff was coming out of the tailpipe. I mean, lead, sulfur dioxide, volatil organic compound, particulates of all kinds of sizes. And as that process got moving, California actually was ahead of the government in many of these sort of tailpipe emissions. We had the end of leaded gasoline, the introduction of a catalytic converter, in order to prove what comes out of the tailpipe. And in fact, I think a lot of people don't really understand how much improvement we have seen on the tailpipe. So I think we should put this slide up right now. Okay, let's put the slide up and examine that. Okay, here we go. It's called Auto Emissions Then and Now. So this slide shows a 1968 four-speed driven by Steve McQueen in the American detective thriller movie called Bullet. And actually McQueen did a lot of his own driving, stuff driving for this film. And if you listen to the soundtrack, which is actually quite interesting, you will hear a lot of double clutching, which you know then the soundtrack was not really related to the movie because McQueen was driving a four-speed, he did not need to double clutch. But I think that the first thing to think about is what's coming out of that tailpipe, right? And in 1968, over 100,000 miles, that car, that's 68 Mustangs, you know, could emit as much as one ton of criteria pollutants. That would be lead, sulfur, voltoorganic compounds, particulates, all this terrible stuff, right? And today, as you can see, these automobiles are a lot cleaner. Maybe a new Mustang probably does not generate more than 10 pounds over 100,000 miles. Wow, that is a big difference. That is a big difference. And the reason I'm showing you this slide is so you understand what the motivation was for California to get what was called kind of special treatment or a waiver to the standards, right? So California was given a waiver on its regulatory program on what it could come up with the tailpipe. And that was an EPA decision that was embedded in the Clean Air Act. California said, look, we have special conditions and those conditions are smog in the LA Basin because we know that even when the Native Americans lived there, there was smog when they barbecued because it's a natural air inversion. So they got that provision. So that provision though is one that EPA could grant. But the CAFE standards, your fuel efficiency, those are actually not issued by EPA. People may not understand this, but those are issued by the National Highway Transportation Safety Administration, or NHTSA for short. So we have these two agencies that are kind of interlocked in a way on this whole regulation of how automobiles perform. And that is the core of what happened this week in Washington. Because on April 1st, the Environmental Protection Agency concluded what's called its mid-term evaluation. And if you recall, at the beginning of the Obama administration, very rigorous CAFE standards were set. Now, what they say they're going to get and what they actually get in real life are two different things. The mileage standards are a kind of modeling exercise. They're not really how the automobiles perform in the real world. But the key feature of those regulations was that if you recall, at the beginning of the Obama administration, the industry was on its back. GM was essentially bankrupt. And in exchange for, you know, getting certain financial concessions from the government, the autos went along with all the stuff, even though they knew they would have a hard time beating them. So we're going to take a short break and reconnect with Lou Pulirisi. He's the CEO of EPRINC, which is an energy policy research organization in Washington, D.C. He joins us every two weeks by Skype, or in this case Zoom, and Voice over Internet Protocol. And we're going to reconnect. We'll be right back to talk some more about the CAFE standards change that happened just this week. Hot news. This is Think Tech Hawaii, raising public awareness. The host of Voice of the Veteran, seen here live every Thursday afternoon at 1 p.m. on Think Tech Hawaii. 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So join us for Human Humane Architecture every other Tuesday at 4 p.m. on Think Tech Hawaii. And we're back. I'm Jay Fidel. This is Think Tech. This is actually Energy in America with Lupu Uriisi, who joins us now by voiceover in Internet Protocol Voice from Washington, D.C. We're going to talk about, we are talking about the change in the CAFE standards that happened just this week. Very important. So, Lup, you were talking about the change and what happened in California and how the basic focus of this kind of emissions control changed. Can you finish that discussion? Yeah. So what I really want to do is, and I think it's illustrated by the Steve McQueen Mustang 68 and 2016 versions there that we saw the photo of. So the question is automobiles have become extremely clean on tailpipe emissions. And when you listen to the discussion, people in California and on both sides say, well, this is really a fight between whether we're going to have dirty air or not. But it's not, that's really not what it's a fight about. It's a completely wrong idea. This is a fight about carbon, you know, greenhouse gas emissions. This is what California is thinking a waiver for. And that's why I told the story earlier, because California got a waiver through the Clean Air Act to deal with smog in the LA Basin, right? And some, maybe San Francisco Bay Area. But now they are using that waiver, kind of what's now called a programmatic waiver, to deal with greenhouse gas emissions. But greenhouse gas emissions are not a local pollution problem in California. Actually, carbon is odorless and colorless. So it's really, you know, there are no particulars in carbon. But California is trying to use this waiver for which the administration believes the wrong purpose. After all, GHG emissions is a global climate problem. Whatever California does on GHG emissions, it's going to have no effect on the climate. So the real fight now is, and if you think about Trump, he's Trump for, he's for populism, nationalism, and industrialism, right? And so the auto industry is a very big, important view of his fate. And so the problem is that for the auto industry, they really want a single national standard. So by this decision, the administration has first said, well, the existing standards are probably, you know, they're going to go through a rulemaking. They have actually not decided what the new standard should be. They're just saying the existing standard, which were heavily back-loaded into the regs, which means that most of the heavy lifting occurs over the next five years, five to seven years. That's not appropriate. It's very interesting how the thing kind of backfired on Trump, because he was trying to serve the automobile industry, saving the money of R&D and the additional costs and cars and the pressure on sales by trying to reach a 50-mile efficiency. So ease it off at 30 miles and put off the whole issue about whether and to what extent to increase it later. That was clearly a gift to the automobile industry. But California is committed. And I would think what happened was really surprised him, is that the states, especially California, which doesn't like him too much anyway, said, no, no, no, we are going to be ahead of you. We have our own standards, and it's a higher standard than you're proposing in retaining the 30-mile per gallon standard. So what he created, he created a problem for the auto industry in that now there would have to be two kinds of cars, one in the center of the country and one on the east coast and west coast. This is not what he intended at all. Well, I think, I don't know what he listened to. I think that's not what he intended. What he wanted is a modified standard for the whole country. But as you say, California is not going along with it. But the question, the point I wanted to make is, well, the rationale, if you like, for California to have a separate standard is not based on the traditional waiver authority because of they have a local smog problem, understand? It has nothing to do with that. That is where the real fight going to take place and how they're going to work this out, we don't know. Remember, the administration has not changed the standard. They have just gone into rulemaking for a new standard. They have just determined that the midterm review, which was put into the law a long time ago, has finished. And the midterm review, they're concluding. The midterm review says that the cost of achieving this standard is bad in a couple of ways. It's forcing people to buy cars they don't want to buy. And it's increasing the cost of the average cost of automobile. And that's actually going to flow the rate at which the fleet turns over. So I think those are the kind of highlights of what the issue is, but there's a kind of inside baseball problem as well, which is how will the court, what will the administration do? Are they going to go to court? Are they going to tell California, look, you might have had a waiver under EPA for local pollution, but this is a national standard that's going to be set in a national highway. Well, just in the four corners of this conversation, it seems to me the administration will go to court because it wants to protect the automobile industry. If the automobile industry has to create two kinds of cars, it's going to be very inefficient and very costly to the automobile industry. So they will go to court and claim that this is a federal area. This is preempted. That the waiver procedure that you described does not apply. And so California should follow the national standard, whatever it is, as far as efficiency is concerned. It sounds like they'll have to go to court, no? Yeah, I agree. And by the way, the net savings and gasoline of this standard and a likely alternative standard is probably not more than, I know, 100,000 barrels to 110,000 barrels a day on a transportation sector that probably is using 9 million barrels a day. So I think they have a case to be made here that, look, the standard itself is not really reducing consumption of gasoline that much. So you're paying a lot for a relatively low yield. So that's one issue that needs to be vetted and explained better. And then the other question is how will EPA propose to modify this standard? So what will be the next step? We don't know yet. Well, one thing is before we had a timeline where everybody could plan. Before the automobile industry here and overseas knew that by a certain date they had to meet a certain standard. Now all of that is in a cocked hat.  Yeah. So, I mean, if you look at, you know, these standards are very complicated and it's very interesting in how this plays out because I do think the administration has a point on the waiver, which is, well, does California really get a waiver for global warming? Yeah, they get a waiver for local pollution, but does the law permit them to take a waiver for global warming? And I think only the courts will be able to settle that. Yeah. Well, I mean, do you feel this is a good thing? I mean, it may only be 100 or 110,000 barrels a day, but that's a lot of barrels, at least in an absolute sense. And this is more of the same from Trump. Right, but I do think that, you know, because Trump is proposing it, I understand how people feel. I have the same reaction. But I do think that, you know, we talked about this once before. If your strategy is, I mean, what is your objective function on this program, right? If your objective function is just to save gasoline, the fundamental criteria for that is gone. We're not relying on foreign sources anymore. We're almost entirely independent. We don't have an energy security problem anymore. So this issue should be legitimately caught out on all the environmental benefits worth the cost. You know, one thing that comes to mind on that exact issue is this. If I were Obama, you know, and thinking through what he did, a move to 50, I would know that it was going to cost the industry more money for that R&D. That is a very hard standard to achieve. And that means that fossil cars will be more expensive. And so I say in the world of consumer choice, this is actually a motivating feature directing people to renewable energy cars, whether they be electric or hydrogen or what have you. And so if Trump had left it alone, it would have been one of those factors that drives the transportation industry to migrate just a little quicker to electric cars. Now I think this is a blow the other way. That taking that standard away and leaving it in a kind of amorphous state, which is what he did, is actually a move to retain fossil cars and not to push on electric cars. Don't you agree? Well, I think that's really what we call, you know, small beer because electric car sales are not more than 1%. I saw that even the Tesla sales were falling off a bit. Yeah, electric, it's not so much electric cars. I don't really think that's the right way to think about it. I think the right way to think about it is that in the end implementing this standard would eliminate a limited consumer choice. You can argue that it's a good or a bad thing. And second, it would have made the average cost of an automobile more expensive anywhere from $1,000 to $2,000 per automobile. That would be the net effect if you look at the data. Maybe they could have gotten better at it. And part of this driven by the fact that gasoline prices are lower and people will want to drive small cars.  They want an SUV. So I think that's a legitimate debate on what, okay, what is the value of limiting the choice? Is it working? Are you getting value for paying more for these cars? Well, let me ask you this though. All of that, shake and bake it, where do you think we're going on this? I mean, a couple of things from this conversation are pretty clear. Right now there is no mandate to go to 50 miles a gallon. There's no deadline by which the government has to decide. So it's going to be stable for a while at 30 miles a gallon as anybody's guess about when it changes. That's one thing. The industry, automobile industry will be happy. Consumers, I suppose, who don't care about this issue, they will be happy. They'll pay just a little less for cars. The environmentalists will not be happy. But where do you think this is all going to go? Well, I think, you know, this issue is really not, if what you're trying to buy is reduced emissions of global, you know, of greenhouse gas emissions. This is a very costly way to do it. It's a global issue. There are lots of cheaper, lower cost ways to do that. And that we have quite a few subsidies for electric cars now. And so I'm generally a person who doesn't really like mandates or requirements. I think that we subsidize electric cars. You know, there's plenty of producers who want to make them.  And that it's a kind of unidimensional environmental calculation. Because to produce these electric cars, we have to power the grid. In many cases, that's with coal. We have to dig up this lithium around the world. Huge amounts of tailings and environmental consequences. And we don't seem to be worried about that. We have a kind of narrow view of the environment. It's not a kind of global calculation. So yeah, kind of Trump is a kind of problematic character in the way he presents the issue. He's very combative. He doesn't take a lot of time to explain the subtleties. Well, there are other implications that we haven't covered. For example, what happens depending on the result and the litigation which you and I foresee would happen in California, maybe other states as well, and whether there has to be two kinds of cars. And there are 10 states that are going to go with California. And finally, how does this affect manufacturers overseas who are trying to sell in this country? They've been ramping up to the 50 miles and now they don't have to. I guess they would be happy. But what's the comparison between the cars they make here and there and not only in Asia but in Europe? So I mean, it's had global implications. Yeah, most manufacturers proceed on their automobile production as a global market. The U.S. is part of a global market for everybody. I can tell you one well-known Japanese manufacturer told me, one of the biggest, they make no money in California, that right now in California, one out of 10 of the cars they sell is hybrid. Under the Obama standards that you like, one out of two of their cars would have to be hybrid. GM, I guess Fiat has publicly said they lose $14,000 on every electric vehicle they sell. Wow. So we have a problem. I mean, the consumers want X. And some people in the environmental community or the government want Y. And we don't seem to have a very good way of sort of squaring that circle. Yeah, amen to that. You know, sometimes you can reach a decision which may have a good basis, at least in somebody else's analysis, but you announce it and you push it forward in a way that offends people. And that's happened so many times in this administration. Even if they're right, they're not handling it very well. But you and I can watch. I could not agree more. You and I can watch and we can see it going forward. I'm sure there's more shoes to drop on this one, Lou. This is going to be a big fight over the next 12 months and there's going to be a lot of negotiations with California. I think some of the administration will hope that California will come to the table and they can reach a compromise on a single national standard because I do believe if you watch the auto company, they kept going around saying, well, these failures are too difficult to meet, but we should have only one standard. Yeah, yeah. One thing is clear that Jeff Sessions will be busy. This will be his second case against California within the last month. Yeah, yeah. This is the federal government versus California. Well, thank you, Lou. The problem is this could drag on for years. Yes, I agree. And we'll cover it, won't we? Yes, of course. Okay, Jake. Thank you so much. Lou Plurici, CEO of E-Princk, who took the time off to talk to us today. So much. We really appreciate it very much, Lou. I really do. Take care. Talk to you next time. Bye.


So, we looked, you know, Friday at essentially what's 1D motion. So, that should have been just sort of a physics one review. We're going to step up a little bit now. We're going to look at in general what we call plane curvilinear motion. Again, we're only looking at the kinematics of the situation, which is just simply the where things are, what they're doing while they're there, and when they're there. We're not looking yet at how we make sure that it's where it's going to be. That's the kinetics part that will follow later. There's three parts to this, or three different ways we'll look at it. It's still, it's three different ways to look at the exact same problem. Different problems, as you can imagine, are going to be easier to look at in certain ways than they are in others. We'll look at the plane curvilinear motion in rectangular coordinates. This, of course, is what you're most used to. This is just simply the x, y coordinate system where, as we watch this, these objects travel along some plane curvilinear path. By the way, plane just simply means two-dimensional. So, what we're looking at is two-dimensional planar motion. We'll put it into x, y coordinates, a little more comfortable for most students that way, but a lot of problems once you get used to the other possibilities that we look at, you'll find that certain problems are much easier to look at in the other coordinate systems we'll use rather than the rectangular, even though that's the one most of us are both comfortable with. I know that's certainly true with me when I just think about things happening. I think about them happening on some x, y plane, no matter what they're doing. But we will find other problems that do better on others. We'll also look at a normal tangential coordinate system. Again, it's a two-dimensional look at two-dimensional motion, and so we'll have two coordinates to it. If we were doing three-dimensions, we see we had the third coordinate. There's not going to be anything new that needs to be done for that third coordinate. It, of course, does make things an awful lot harder to draw. We'll also look at what we call a polar coordinate system, and that's generally something like r-theta. And so, again, just two, two coordinates to it, but a slightly different way to look at the very same things. All right, so we'll look at general plane curvilinear motion in x, y space. So we'll need some coordinate system. Again, the origin, as always, is arbitrarily chosen to be most useful to you, most useful to that particular problem. It could be a completely different place than some other problems. And we'll have some 2D curvilinear path across that plane, and it's the motion of the object along that path that we're going to concern ourselves with now. It's location at any time, you know, it's going to be a little more easy for me, I think, as I draw this, if I just put it up, same thing, just do it in a white so that the colors then are a little more useful. So if we have an object at time 1 happens to be there, we locate the object with some position vector as described in x, y space. So it'll have some dimension x1, some dimension y1, and it's those two together that will define the position vector that locates that point for us. Not terribly unlike what we did in physics 1, with the standard unit vectors i and j to give direction to those two components there. Presumably at that point it'll have some velocity along the path, so we might call that v1. At any point along the path the velocity vector is tangent to that path. It'll become a little more clear in a little bit just how we prove that, but feeling to your common sense of it, if there was any component of the velocity normal to the tangent, then that component of velocity would actually be taking it off of the path at that instant. And that wouldn't make any sense for it to follow the path. For it to be on the path, it cannot have any sideways component of its own velocity at that instant. We'll be a little more clear just how we can say that when we get to normal tangential components a day later. And then of course the velocity vector itself is the time rate of change of the position vector, illustrating it for a point 1, but it's generally the case anyway for any position along here. This will apply. And then that's the time rate of change of each of the individual components, different possible ways that you might wish to draw this. My recommendation is that you get used to this dot notation. It's very, very useful, especially as we'll see in a second or two when we do a particular type of problem. In case that's not enough, we could also override it, written it as the x velocity vector component plus the i velocity component vector at that point. Specifically, which one of these notational forms you work in, I don't particularly care. I'm not going to put all of them down every single time. That's just going to take too long to be a big way to effort. But I will typically use the dot notation because I find it very, very useful as we'll see in a little bit. Sometime later, that object may have moved here to some point 2, now described by a different vector and now with a different velocity. But remember, always tangential of the path at any instant. As that undergoes that change in both position and velocity, of course, has an average acceleration which is the change in the velocity vector as time goes by because presumably it took some certain amount of time for it to go from point 1 to point 2. That's the difference in these two velocity vectors over some particular time period. And those two velocity vectors, we can get the delta v by subtracting the two vectors. So I'll very accurately bring it over here. That's minus v1 because now I can have v2 plus a minus v1 and I get the change in the vectors. And then that then becomes the delta v vector that we use here. Divide that by the time which is a scalar, of course, and then we get the average acceleration vector. Might look something like this. A different color than the delta v vector because it is a different vector. A different length could be shorter, could be longer. It's going to be drawn to a completely different scale. But they are parallel because the acceleration vector is always going to be parallel to the displacement vector from which it was calculated. That's just the nature of multiplying by a positive constant. The two vectors will always be parallel no matter when they were drawn. That in itself, drawing didn't come out particularly well just by coincidence, will have an x component, a y component to it. It cleans things up a little bit just to illustrate why we have to be particularly careful with curvilinear motion in x, y space. I'll take off all of those preparatory vectors we had to begin with, the position vectors, the two velocity vectors. Just pick one point on here that we might have been looking at, maybe this was the third pointer, the second pointer. It doesn't particularly matter. We could go through this very same analysis we just did to figure out what the acceleration vector is. For the sake of argument, let's say it came out to be something like that. The two components that make that vector up, the x and the y components, their directions are specific to the coordinate system chosen. They have nothing to do with the particular path taken other than they come from it. So in this case, this would be ax3. The 3 just happened to be the point we're talking about, x the acceleration in the x direction, this the acceleration in the y direction for the point of interest we have to be talking about. Even though at times it may look like it, neither one of these vectors is the centripetal force, sorry, the centripetal acceleration vector commonly associated with motion along a curve. You remember from uniform circular motion that at any time we have a point moving on this circular path at constant velocity, there will be a centripetal component of the acceleration directed directly towards the center. If it's not uniform circular motion, then not only is there this component due to the curvature of the path, but there may or may not be an acceleration component along the path as well. That's a different setup than we have here. There are times where this vector, showing us the acceleration at a particular point in time, might look like it's pointing towards the center of curvature, but that's coincidence as much as anything. Same thing for the two components. Every time we go along a curved path, there is some point that represents the center of curvature for that path for general curvilinear motion along any general path, the center of curvature is going to change instant by instant because the curvature of the path itself is changing instant by instant. For example, down here, the center of curvature might be someplace like that. If there's a straight section for a little period which it looks like there might be here, a little bit of period where there's no curvature to the path, then the center of curvature doesn't exist or is at infinity, however you want to look at it. And then later in here, the center of curvature might be down here, and over here, if the curve tightens up, turns over some, the center of curvature might have moved. So the center of curvature is constantly moving itself because the path is a very general path. At any instant in time, there is a centripetal component because that's just the nature of travel on a curved path. But when the component directions themselves are set by an arbitrary coordinate system, then there are times when it might look like any of those are the centripetal component of the acceleration, but it's most likely just coincidence. You have to keep this vector in the X, Y coordinate system when working with an rectangular coordinate system. To maybe further prove the point, at any time we can change the angle of the coordinate system that will change these components depending on what the orientation of the coordinate system is, but the vector itself does not change. Only the component representation of it will change. So be careful, sometimes the coordinate system can give you slightly different appearing results if you're not careful with it. Careful with your drawing and careful with your analysis. So we've got all kinds of other ways and we can show that my personal preference again being this double dot notation. And if this is the average acceleration vector, these are average components as well. All right, quick problem. Jet has some takeoff path, something like that. It's not a coincidence that this jet looks like the car I drive because my car can turn into a jet, it's pretty cool. So we've got some path there and we've described that path in X, Y space as being something like 0.01 X squared. So it's, sorry, it's Y position. It's height above the ground in this case is described as a very shallow parabola. All right, given also that the altitude is increasing steadily at about 10 meters per second. And I want to find its velocity and acceleration at a height of 100 meters. So at some particular point, 100 meters off the ground, we want to find its velocity vector and acceleration vector. Let's see, velocity vector, that's the rate at which the two component directions themselves are changing. Now let's see, how are we gonna handle it? Let's see, Y dot is already given where is that? Altitude is increasing steadily at this. So Y dot is given as 10 meters per second and assuming that it's fairly constant. So the jet is gonna clearly have a changing speed along that path for the vertical component to always be constant. X dot's a little bit different. We're gonna have to come to it in a less direct path. That was just very simple. It was simply given. Y dot is also the time rate of change of this position vector as given. Sorry, that position, the path equation as given. That's also Y dot. Well, we can do this differential. We can do this derivative. The constant comes out. The inside portion, the derivative is, well, we gotta use the chain rule on it. Power comes down, reduce the power by one on the root and then the derivative of what was inside and we get that. So there's our X dot there. So the Y velocity is actually a function of not just position, but X velocity as well. So X dot, we can solve for it, is Y dot which is given over X where X is the position here, but we can figure out what that is as well because we know we're in an altitude of 100 meters. We'll know where the range is when we're at that height of 100 meters. So we can find that value as well. Y is 100 meters. X must at that time then be, what was that, 316 meters, I believe. When you solve for that. Now we'll check down, 316.2. So we can get the X component. We've already got the Y component. We'll have the velocity vector in rectangular coordinates even though the path itself is not a regular path through that. So the pieces go in. X is 316. And that comes to be 15.8, I believe. And so we have the velocity vector as X dot I, X dot's 15.8. Y dot J is 10. And we have the velocity vector. And we could draw it on that point as expected it's, well we already know it's got to be tangential. It's just now we know what those components each are. So that's Y dot, that's X dot at the point of interest in the whole thing is gonna be. So good thing we made you take calculus before we got here. You wouldn't know what the chain rule was. Questions about that part before we go to the acceleration? How are we gonna find the acceleration? How are we gonna find the acceleration? Recommendations? DET of velocity vector. Keep derivorating. When in doubt, derivorating. Okay, we've got that vector. Actually, this is a specific vector. We need to use the changing vector. We need to take the time derivative. Not of that, that's just a constant because it's only at a single point. We need to see how things are changing. So we need to use X dot and Y dot. Let's see, the form we need to use is these two, Y dot. Well, X dot, yeah, X dot we've got and Y dot in terms of that. And we can take the time derivative straight away. Got all the pieces there. This of course being the fiber here. This of course being double dot R if we're looking for it. Make sure you have the pieces there. Okay, we can do that derivative. Time derivative of X is X double dot in the I direction plus the derivative of this term. Oh, sorry, there's supposed to be a J in there. That's the Y component. So make sure you get a J component, a J unit vector in there. The time derivative of that piece, again the constant comes out in front and then we have to use the chain rule on these two pieces. X plus X double dot, that's the first part plus the times the derivative of the second part plus the second part times the derivative of the first part, a J. Now, here's somewhat the beauty of what we are given. What is that equal to? Zero, Y. Remember, this is Y dot, Y dot is constant. The altitude is increasing steadily. Y dot's a constant. The derivative of that is zero. So we can use that then to solve for X double dot. X, remember, is the position at that point. We've already got that, that was the 316. X dot at that point, we've already got, that's the 15.8. The only thing we're left with is X double dot and that is minus 0.791. Put that all together. We already have this, is there a question? Got the acceleration vector. Anthony, you're frowning. Where'd you get the X double dot, X plus X dot square? It's right here. That's from the chain rule on the Y portion. Took the time derivative of the velocity vector. The Y portion, I need to do the chain rule on and that led to this term here, actually this whole term in brackets. And so we have then the acceleration is minus 0.791 I, here's the first second square. Which is completely in the X direction drawn to whatever scale we might draw to. Notice that that is not a centripetal acceleration because one, the center of curvature doesn't lie along there. You'd expect it with that kind of curvature to be way up there somewhere. That'd be the radius of the circle it's on, the curve it's on at that instant. So that's just the acceleration vector in X, Y coordinates. Some other coordinate system will still have that acceleration but the components might be different. Yes, this is X dot, the velocity in the X direction squared, which is this 15.8 squared. So that's 100 meters, no, 316 meters. That's the X position at the point of interest. X double dot we're looking for. X dot is 15.8 squared and those two together are zero. Fair enough. All right, any questions on that one before I clear up? Go a little bit more. Stop the tape, take a break. Recton linear motion, besides just the general type we looked at there, is projectile motion. Always takes place in a plane with the down direction defined of course by gravitational motion. Typically, not typically, realistically, the acceleration in projectile motion is a function of the velocity due to air resistance effects. We're not gonna deal with that. We could do the very same approximation you did with me in physics one if you had me for that. Where we approximated that kind of motion. But we'll look at a more idealistic setup where the acceleration in the Y direction is a constant and of course that constant being the strength of the gravitational field or G. If you had me for physics one, this is the way we did projectile motion problems. It's also part of reason why I prefer this dot notation that we use. So for any given projectile motion type problem, it is a planar rectilinear type motion. It always occurs in a single plane. Only way you could have it occur in a three dimensional space is if there's some kind of sideways component of force, either this projectile is flying through a crosswind or it's a powered flight of some kind. These are completely unpowered, unpowered flights. This is what's known as a ballistic trajectory. The term ballistic means unpowered. If we're using a rocket of some kind, we don't start this part of the problem until the rocket's shut off. Which means the only force in the problem is that of gravity. And hopefully you remember from physics one, what we termed that kind of motion. Where gravity is the only power. The only force in the problem. That's, this is also known as a free fall problem. So we'll take the trajectory problems in this class to be free fall problems. Unless there's some other part to the problem that is very obvious in the problem. A parachute, some kind of jet engine or something attached to it. Or if air resistance is included. All right, we'll take a, you stop the tape for a second if you want. All right, all projectile motion problems no matter what they are. Whether it's from a higher elevation to a lower, to an even elevation between the landing and the launch. Or whether it's from a lower elevation to a higher. None of it matters. They all solve in the very same way. They all involve of course some launch velocity. Often termed a muzzle velocity if we're using guns or cannons or something to do this. Some launch angle or elevation as part of that. And then they all solve in the same way. For my physics one students, what did I always do next? Divide the problem into two parts. Divide it with what? Semi permeable membrane. A semi permeable membrane. And we keep the parts separate from each other. We have a horizontal part and a vertical part. And these two are happening independently. It's not the case if we take into account air resistance, but for a free fall problem they happen independently. And it's all based on the fact that the acceleration in the vertical direction is zero. There is no acceleration in the vertical direction because of the fact that it's both an unpowered flight and it's without air resistance. Vertical acceleration is constant and we take it to be known.  So we'll use G. If it's a problem on some other planet then you'll need the gravitational field strength in that way. The minus sign. That minus sign is not a feature of G itself. It's something I arbitrarily add just using the downward direction as negative. I don't have to. I can do exactly the same problem some other way.  Every other part of the problem has to agree with that though. As a consequence of the zero velocity in the horizontal direction, sorry, zero acceleration in the horizontal direction, we know that the velocity in the horizontal direction is constant. It must be if there's no acceleration. Not only is it constant, but we know something more about it. It's the horizontal component of the launch velocity. This, I don't care what type of projectile motion problem you're doing. This is always true, what I'm putting up here. And all you have to do is fill in the little parts and solve for the things you don't know. Whatever the unknowns in the problem are. Acceleration, velocity and position. How do we find the position of an object traveling with constant velocity? It's that velocity times the amount of time that was in the air, so it's nothing more than that. That's the entire horizontal side. There's nothing more to do with it. Well, there's some terminology we might need. This is typically called the total distance of travel in the horizontal direction. It's typically called the range. So you may be given a problem that says that a range of a projectile or ballistic missile or something is such and such. You have to interpret that to be the total x travel from where it started to where it finished no matter what the altitude of either one of those points. Because there's no vertical consideration in this. Notice, as we're doing this, the obvious nature of my preference for this dot notation, there are only x's over here. Horizontal motion is the x direction motion if we put a rectangular coordinate system to it. And there's no y's over there. So it helps you keep things straight. You're gonna have a lot of velocities in this problem. It's very easy to confuse them if you don't have a semi-permeable membrane down the middle of your paper. All right, if the acceleration in the y direction is constant, what's the consequence then of the y velocity, the vertical velocity present? How does it change or does it? Of course it does. If there's acceleration in the y direction then the y velocity is going to change. How does it change? Linearly, it's a linear change. If that's a constant, then the derivative before it is a linear and that would be y double dot t or minus gt, not quite. What's missing? You need to add the initial. Yeah, if there's any initial velocity, y dot zero using zero for the original pieces. And that itself is the vertical component of the velocity. We have to put a subscript on that because it does change. It starts out at v zero sine theta but changes from then on in this linear fashion. Constant times a variable plus a constant is a linear description of the motion in the vertical direction. And then the vertical position itself as a function of time, vertical position as a function of time would look like. And that would change exponentially, right? Nope. There's an exponent in it, yes. There are a moment. It's a quadratic change. It's quadratic. One half gt squared plus y dot t plus any initial altitude. But I typically just make this a delta y over there, put the initial height over there. Then you're only concerned with the change in height and just sort of reduces things by a single variable. Any other constant acceleration equations. This is one of the constant acceleration equations. There are three others. They all apply in any way you might need to solve that side of the problem. What about here? I didn't bother writing down and any other constant acceleration equations. Once you put a equals zero into any of those equations, the only one you're left with is this one anyway. Everything else disappears. So both sides are constant acceleration problems. This one by far the simpler because the constant acceleration happens to be zero. This one just becomes a regular 1d constant acceleration equation. Semi permeable membrane because three things can cross either side. The time is on both sides. So is the launch velocity and the launch angle. Those are the only things that can cross the semi permeable membrane. After that, all you have to do is take any problem you're given and find out which of these pieces you have and which you don't. And if you can't find one of the pieces on one side, you usually can by finding something on the other side and bringing the t or the theta or some other part of it over. So let's look at a classic projectile motion problem. And these do very well in x, y coordinates, rectangular coordinates. It's the way we started with them in physics one and it's the way we keep going with them as we finish here. All right. So imagine some kind of basketball shot or something such that the shooter is able to hit the basket 2.5 feet above where he releases it a range of 25 feet. His release velocity, the magnitude is unknown because we got the tapes from ESPN and figured it out from there. Now, of course, once the ball is out of his hand that is a ballistic trajectory because it's unpowered flight other than under the influence of gravity. So given that little bit, we want to try to find two things. We want to find two things. Find v0 and that's not going to be much more than identifying what's known over here and solving for v0 is the unknown. There'll probably be another unknown to find it but that's okay, you'll have enough equations for doing so. And find phi, the angle, curve makes as it goes through the basket. That's important because if it's too shallow the ball wouldn't actually fit through the hoop. It might make it through the hoop after it bounces around off a little bit but it wouldn't cleanly go through and so you need enough angle on it there to make sure the ball would cleanly go through the hoop to increase the chances of points on the board in the adulation of cheerleaders nationwide. It's a pretty low basketball. Now that's just over, that's the height above his hands. Okay, so girls come to the court.  Alright, so to find v0 you need to identify what parts of this we've been given and then what parts of that we can use and then solve for v0. It might come straight away from either side of the equation because v0 appears on both. Alright, what things are given besides the two accelerations, what things are given and each one of them will have a place over there either directly or indirectly. Where can we put these numbers? 25 feet. 2.5 feet. 50 degrees. Don't be shy. You know I'm not a camera man. Which is the 25 feet? It's actually this. The total x distance. So delta x is 25 feet. X is 25 feet as well if we take x1 or x0 to be 0. Just start the, we'll put the origin at the launch point which I've already done. What about the 2.5 feet? It's delta y plus or minus. Plus or minus. I heard one vote. Thank you for speaking up. I appreciate it. Is it plus or is it minus? Delta y plus 25 or minus 25 feet. It ends higher than it started. That's all you need to know. It's plus 25 feet. Any projectile motion problem we can handle in any way if we do it in this form. 2.5. Sorry 2.5. You can see it but there was a decimal point there. I just had to emphasize it. All right. What else do you know? We know some good parts of this. We don't know the initial velocity but we do know the launch angle. We can use that in here with this 25 feet as the total distance. So we don't know v zero but we do know the launch angle. So at any time t it's going to be at some position x. At total time it'll be at x equals 25 feet. Over here, what else do we know? Same kind of thing for the launch velocity. Remember we don't know the v zero so we don't know that launch velocity but we can use that in here. We get a position as a function of time and we put that initial velocity in there. Are we getting closer? Notice the basket. We know that x is going to be 25 feet y is going to be 2.5 feet that gives us two equations with two unknowns. v zero and t are the only unknowns. It pulls 2.5 feet. That with the last two equations gives you two equations, two unknowns and it's a system you can then solve. When you do so we won't bother with the here because this isn't a class in linear systems. Actually it's not a linear system. 1.3 seconds. Give or take a little bit of velocity you should be able to solve for 29.9 feet per second. Amazing.  What about the last part of it? This angle with which it hits the basket. You take a little bit of time and figure out what that is. We'll let's see. We won't necessarily have time to go into another problem but we'll make that a get out of class question. You get this angle assuming I have it right in the paper. You get this lawn, this landing angle. Travis, do you have it or are you thinking? Okay. Good. I thought I smelled something burning. If you find the angle with which it enters the basket then determine whether or not all would actually make it through cleanly. Possibility of a little swish or you're going to hope for a rebound. Who's got a plan? Zero. Anything we can do? Notice that over here there's nothing in here that says what the final angle is. Only the initial angle. That's what theta is. It's the initial launch angle that we had there. I'm asking for a different angle. What are you right there? David, you got it? No. You know what to look for? See fairly straightforward now that you have those two pieces. That seems relatively busy. That means there's some progress being made. Alan, okay? Got an idea? Give it to him. It's not a test. If you need to ask a neighbor what they're doing feel free because basketball is a competitive sport. Doesn't mean that engineering is. At least not competitive in here. Anthony, got an idea? If we look a little more closely at this piece here we've got the ball coming into some angle and we're interested in what that angle is at that last instant. The 25 feet down range, 2.5 feet up. At that instant it has that velocity. Nothing over here directly gives us anything about that angle that it's making. However, we do have ways to find we call this 0.2 x dot 2 and y dot 2. If we find those two components then we can find this angle because it's that angle. If you find the two final velocities in either direction then you can find the angle. Right, Chris? You did it? You don't like me to come to you. Because you'd like to stay no matter what. You don't have to kick you out. How come you never get what I get? How come you and Travis never get what I get? 0.2 Well, this x dot's a constant, right? And so what did it come out to be? 0.2 Good, we agree on one thing. 19.2 meters per second. Now remember that x velocity is constant the y velocity and I can't see the numbers you use there. But Chris, you put in the wrong g. Did you use 9.8 for g? What's g in the English system that God gave the world? 32.2 feet per second squared. That was on Moses' third tablet the one that he dropped on the way down which is why the metric system is getting in there. You see where it leaves that in the tape. David? Yep, that's what I got too. Better? Yeah. How do you find y dot at this point? Well, we have an equation for y dot. We know the acceleration. We now know the initial velocity. We can find the velocity at that time. Shouldn't be positive or negative. Or does it even matter? Better be negative because it is going down in the y direction at that time. Alright, there's still a little time to get out early. David? Do we go early? Chris, you got it now? Oh, say it out loud. Get out of the class question and just blur it out. You just qualify yourself if you have to stay. But yeah, that's what I got. Stay in. What? Go through the physics lab. What am I doing with that? Because I don't think it's locked from our side. I think it's locked from the other side. Okay? Alright, let's see. Let's put the last little bit together. Then we can all get out the class on time. Alright, we'll need those two pieces that we came up with from the first part of the question. The x velocity component. This is the final velocity. The x component we already know because it doesn't change. Once we are v0, we know what x dot is. What was v0? 299. Times cosine fifth. That's the x component of the velocity. The y component of the velocity, it's always changing and it changes to the tune of this one equation. Minus 32.2. That's the acceleration. Don't fit the minus sign of this down. Times t, which is 1.302 seconds plus whatever initial component we have and that we've now got because we have v0. Remember that sine 50 degrees is not the final angle. It's just the initial angle, the initial component that gives us the launch there. And I believe that comes out to, that comes out to 49. This comes out to be like minus 19, which is very, very close to the other component so this comes out to be about 45 degrees. Give or take a little bit. Hopefully that's the home team, but Timberwolves gets in and that's a wrap.


s a 99 kd come on rookie caller come on rookie caller tri-color concourse rookie jalen durin he's had a great start to the season jalen durin he's had home grand very nice rookie maroon premiere level 44 of 175 awesome chet this card nicholas thank god we don't have that jim would jim would order it i know it and then you'd have to wait a full day for sam to rip it because i ain't doing it but sensations of jubar so the junior silver concourse nikola yokic although i'd be sure if i didn't have to wake up at like 945 i would yeah i gotta do it while i'm back in the whole place out tonight so it's one of the nights mathron concourse come on nice auto that's pretty solid jonathan kaminga to 249 on the in-flight second-year auto nice kaminga that is a scope concourse of anfrony simons it's a nice chat i've been to the nicest card so far kaminga solid auto yovitch that's a silver premier level jalen brunson then i feel back to them not for sam ruffin jim because samby ruffin is working yeah exactly isika coro to 99 on a jersey auto here coro good player nice got the copper um what is it called copper checker to 49 is van vleet sga unstoppable insert thunder silver premier level dyson daniels rookie card come on last two packs come on future nemar tricolor concourse demar to rosen jalen green he can marry concourse jabarry smith junior concourse scope rookie that will do it appreciate you nicholas decent box there's hope for something bigger for you but got numbered chat rookie pretty darn good and get it out to you all right we got greg and jim last couple tonight everybody gonna take us to about 140 or so maybe so hungry and try not to eat anything when i got home oh i'm like i will try to eat the just maybe i'll find something to just devour we should have jake race the cranes outside be worse if you'd fall then they'd like attack everybody forced here got an awesome three box football mixer here for gregory h 2022 nc hobby 2023 gold standard hobby and 2022 origins hobby appreciate the orders man let's start with the origins and we'll do a gold standard and then to the nt origins football coming out i think this week all right got karson went to 299 75 hollywood brown schkelenard and tyreek hill let's go pat how about that gorgeous patch 12 out of 49 to a tongue of my loa the recolor fins patch there go pats this guy's been playing pretty good actually Mcbride rookie auto 299 he's been pretty good he's got Mcbride color match auto 299 neon card and then adan hudgensen rookie jersey auto solid box of 22 origins for sure hudgensen rookie jersey auto you uh carnells fan harp go hudgensen there too finna let's go fins baby fins let's go 23 gold standard g-harps my dude dude how are there so many dolphins fans you're seeing them now because we're finally doing good they're coming out that's high because we've been stuck in it 40 years what 43 years i don't know if he is him enough of them too man chat it's all fully it's got texted it's 130 bro 49 is mike will this guy's pretty good too sam la porta rookie out of 99 mother lode five-way jersey to 299 isai apacheco newly minted rookie jersey jaden reed that's out of 299 he kind of went off last week didn't he jade and reed it's not a dynasty football team um jersey card to 299 justin jefferson rookie kicker action here is a jake moody auto to 199 jake moody solid one there kicker staff's sticky value sometimes and a cedric tilman dual jersey rookie out of 149 hoping for a digger auto on the back there let's see what 22 nt has real great let's see a nice qb true rpa starting it off treasured rookies brice hall to 99 that's a pretty solid start that dude's an animal he like is the jet's offense brice hall to 99 mark andrew's number to 15 dual jersey to 25 is uh charles hayley player worn hayley dual jersey card rookie dual patch garret wilson 11 of 17 yeah double patch card garret wilson offensive rickie the year last year framed fabric out of 25 is um uh kyle you check juice a treasured patches to 10 justin jefferson now last relic all autos from here on out jettas to 10 first auto this guy was thawed antonio gates 92 of 99 that was sons at michigan state antonio gates auto to 99 andre badmoon rising auto to 99 badmoon rising and at a 25 a justin jefferson autograph j jettas 7 to 25 25 minus 7 jersey number boom there you go brew rpa amad sauce gardener 88 of 99 three color true rpa that's pretty damn sick right there there we go greg that's awesome man that's awesome i mean if there's a defender to get he's probably it right him or hutch on a true rpa that's awesome man yeah definitely definitely good box there definitely good box that will do it good stuff buddy thank you thank you we'll get him out to you i mean if you buy another nt i'm gonna rip it all right jim it's time let me get gregory's uploaded and then uh time for photos yeah for three bucks i was i was pretty solid it's pretty solid a true rpa have a really good player you know even if it's not a monster offensive name that's good that's good well this is the last one in q so once this is done if nothing else is there we out i was going everybody forced here we've got a personal box of 22 23 in the war basketball first off the line for jim l right here so we're gonna get that silver framed first off the line or no gold frame to 11 excuse me gold frame to 11 first off the line and then should have four autos in here as well all right let's do this the gold frame is the first off the line exclusive all right now the fun part getting the cards out of the box i know i should see how this goes come on give me like more than two cards here come on like a glove that's a nice card one of these i just gotta break easy there we go come on come on then i want you to see that top guard that thing is sick okay there we go the card's too nice the card's too nice okay all right easy does it there we go man oh man what a what a packaging is done you have to destroy the box to get it open okay here we go here we go jersey card of 99 rookie jaylin williams on the elegant decor rookie jersey j-dubs good j-dubs good auto right here walley zerbiak to 99 freeze frame signature is walley zerbiak was pretty good for a few years of the wolves and i think a little bit with the Celtics right nice walley next is rookie auto number two 99 ooze monjang on the showtime signature here and i saw your order greg back in the saddle rookie patch auto out of 99 david roddy david roddy rpa this might be the nicest card in this box it is sneaker spotlight signatures anthony edwards 32 of 99 jim what a gorgeous card dude that is freaking sick and edward sneaker spotlight sig i mean these things are just too pretty oh man gold frame coming up in a bit here jersey jumbo og on an obi to 99 og on an obi desmond bayon on the newsreels jersey to 75 bets are game used gold frame rookie johnny davis six of 11 on the statement edition gold frame six of 11 johnny davis we're gonna go bare to 49 on the base association edition icon edition to 49 kevin porter jr so they'll base on the bottom interesting and a steve curry to 99 you congrats on that ant man made the box pretty good we'll get those out to you jim thank you thank you i'll be a sig all right guys this is the last one tonight the for real last one tonight we got a g harp see if you can top the sauce it's from the same case so could still be a qb rpa in play could be everybody forest here got a box of 2022 nt football hobby for gregory h appreciate the order gregory here we go buddy the sauce last time let's see what's up this time bless you we're like over there again guys kyle and jake are live in about eight hours all fanatics live sam will be live here four eastern tomorrow you got a 10 hour stream here see that we live for 10 hours so no doubt hey gris all right first up is going to be andre johnson and 99 andre johnson a joe nameth midnight base parallel one of 20 one of 20 joe nameth midnight rookie dual jersey to 99 is going to be aiden hushinson hutch to 99 patch card is uh to 25 excuse me to sean watson sean watson at 25 dual jersey is for the uh the jets legend here ladenian tomlinson number to 25 ladenian tomlinson player worn to a patch card seven of ten three colored to a patch player worn the dolphins sunday morning dolphins this week yeah they're gonna lose by by noon crazy catch the last three minutes again or something yeah end of the autos now rookie auto nukobi dean to 35 kobi dean nukobi dean this guy's a monster right here that is to 25 jonathan augdon autograph 10 point went dolphins let's go i i can see it let's go augdon auto to 25 let's go patriots no let's go pats that's the thing it's true it's very true uh true rpa here is going to be isaias spiller to 99 three color true rpa nukobi dean is definitely like the he's a middle linebacker right he's a good player isaias spiller to 99 true rpa there and a sam howell rookie material signatures 81 of 99 there's a qb we're looking for 81 of 99 sam howell see how he does against the patriots nice sam howell got the spiller true rpa nukobi dean auto there we go nice and how we'll get that in a mag we'll get that out with the other stuff Gregory thank you again thank you again all right a couple of solid boxes i would say a couple of solid boxes i'm gonna get that upload of guys then shawna that are gonna get out of here i'm sure informatics live chat tomorrow i'll see you there i'll be in chat a little bit here tomorrow evening as well i'm gonna try not to work too hard on my day off yeah g harp it was it was it was pretty solid overall for sure hey see you christ you strive aurora g harp jim all those that are still hanging out it's a late one yeah we'll be live at 10 a.m all fanatics live take care everybody have a fantastic weekend


Now being in school and in medical school all the way up to the age of 25, I've pretty much been in school trying to get the grades and stay away from the medical debt. And throughout the process, as I was spending hours and hours studying, I was also seeing on social media or my peers at my same age, we're getting new houses, starting families, having kids, having beautiful cars, and saying, man, I wish that could be me. But then I realized that the benefit of delayed gratification is that whenever I would have a level of success, that dopamine hit wasn't as high. And I was always focused on going to the next thing, instead of being super excited for something and then let down when the feeling was over. And so my personal experience, I'm much more excited of rolling a bunch of snow and making it a huge snowball versus getting the huge snowball ASAP. And that's allowed me to have a greater appreciation for the things that take time. For example, in investing where initially I started with absolute zero, my wife and I got married to now just three years down the process where we have a six figure investment portfolio, things like fitness where I could barely run a mile several years ago. I just ran my first marathon in December of 2021. I'll be running a half marathon a week from now.