'''
Projectile motion

Although it is nice (and valuable) to calculate the range of projectile 
motion by hand, it is much more convenient to write a program that allows you 
to study this motion and do various calculations within a few seconds. 
The basic equations are:

x = v_x * t = v * cos(theta) * t
y = v_y * t - 1/2 * g * t^2 = v * sin(theta) * t - 1/2 * g * t^2

where `x` and `y` are the respective position components, `g` is the 
gravitational constant, `t` indicates time, `v` is the velocity of the throw,
and theta is the angle the ball was thrown at.

Exercise A: 

Plot the projectile motion for theta = pi/3, v = 100 m/s and time 15 seconds. 
'''

# Your code here

'''
Exercise B: 

The above plot shows the projectile motion, but does not stop at `x` = 0. You 
can solve these equations for t_max and x_max:


t_max = (2 * v_y) / g = (2 * v * sin(theta)) / g
x_max = v_x * t_max = (2 * v_x * v_y) / g = (2 * v^2 * cos(theta)) * sin(theta)) / g


* Write a function which returns x_max as a function of inputs theta and v. 
* Make an array with 20 evenly spaced angles theta in the [0, pi/2] domain, 
using `numpy.linspace`.
* Plot x_max as a function of theta for v = 10 m/s. 
* Additionally, plot x_max as a function of theta for v = 20 m/s. 

From the two plots, which angle is the best to reach the maximal x_max?
'''

# Your code here