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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Projectile motion
The trajectory of an object in projectile motion can be described by 
$$ x = x_0 + v_{0x}t$$
$$ y = y_0 + v_{0y}t + 0.5gt^2$$
Which says that the object will move at constant velocity in the horizontal direction, but with acceleration vertically. 
In order to visualize this, we will use vpython. For that, first we want to import this library
Step1:  Now, let's create a screen showing a ball of color red and initial position $x_0$, $y_0$
Step2:  Then, we want to assign a small time step to see how the system evolves in time. And the system should evolve until the ball hits the floor
Step3:  Look at the path the sphere followed. Is that what you where expecting to see? 
Air resistance
Now, let's make a more realistic model. Assuming that the force caused by air resistance is directly proportional to projectile's velocity, with k retarding force constant. The motion is described by the following expressions   
$$ x = x_0 + \frac{v_{0x}}{k} \left( 1 - e^{-kt} \right)$$
$$ y = y_0 + \frac{-gt}{k} + \frac{k v_{0y} + g}{k^2} \left( 1- e^{-kt} \right)$$
Let's see how this looks like
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Python Code:
from vpython import *
import math
Explanation: Projectile motion
The trajectory of an object in projectile motion can be described by 
$$ x = x_0 + v_{0x}t$$
$$ y = y_0 + v_{0y}t + 0.5gt^2$$
Which says that the object will move at constant velocity in the horizontal direction, but with acceleration vertically. 
In order to visualize this, we will use vpython. For that, first we want to import this library
End of explanation
#initial position
x0 = -10.0
y0 = 0.0
#create canvas "screen"
scene1 = canvas(title='Projectile motion demo', width=600, height=300, center = vec(0,0,0))
#create ball
ball = sphere(pos = vec(x0,y0,0), radius=1, color = color.red, make_trail = True, trail_type="points")
#initial velocities
vx0 = 5.0
vy0 = 5.0
#define where the floor is
floor = - 11.0 
ball.velocity = vector(vx0,vy0,0)
Explanation: Now, let's create a screen showing a ball of color red and initial position $x_0$, $y_0$
End of explanation
dt = 0.01
t = dt
while ball.pos.y > floor:
    rate(100)
    #note Projectile Motion equations are here! 
    ball.pos.x = x0 + vx0*t
    ball.pos.y = y0 + vy0*t - 0.5*(9.8)*t**2
    t = t+dt
Explanation: Then, we want to assign a small time step to see how the system evolves in time. And the system should evolve until the ball hits the floor
End of explanation
x0 = 10.0
y0 = 0.0
floor = -11.0
scene2 = canvas(width=600, height=200, center = vec(0,0,0))
#create 2 balls at the same initial position
ball1 = sphere(pos = vec(x0,y0,0), radius=1, color = color.blue, make_trail = True, trail_type="points")
ball2 = sphere(pos = vec(x0,y0,0), radius=1, color = color.red, make_trail = True, trail_type="points")
#initial velocities
vx0 = 5.0
vy0 = 5.0
ball1.velocity = vector(vx0, vy0, 0)
ball2.velocity = vector(vx0, vy0, 0)
k1 = 1.05
k2 = 0.005
dt = 0.01
t = dt
while ball1.pos.y > floor:
    rate(100)
    #note Projectile Motion equations are here! 
    ball1.pos.x = 
    ball1.pos.y = 
    t = t+dt
    
#t2 = dt    
#while ball2.pos.y > floor:
 #    rate(100) 
  #   ball2.pos.x = 
   #  ball2.pos.y = 
    # t2 = t2+dt
Explanation: Look at the path the sphere followed. Is that what you where expecting to see? 
Air resistance
Now, let's make a more realistic model. Assuming that the force caused by air resistance is directly proportional to projectile's velocity, with k retarding force constant. The motion is described by the following expressions   
$$ x = x_0 + \frac{v_{0x}}{k} \left( 1 - e^{-kt} \right)$$
$$ y = y_0 + \frac{-gt}{k} + \frac{k v_{0y} + g}{k^2} \left( 1- e^{-kt} \right)$$
Let's see how this looks like
End of explanation
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