"""
Exercise 5.13 from "A primer on..."
Plot the trajectory of a ball. The task is
made slightly more complicated by the
fact that we are supposed to plot for y >0,
which means that we must solve the
equation f(x) = 0 to find the upper bound for
x. The equation is quadratic, so the solution
can be found using the standard abc-formula
for quadratic equations. 
"""


import numpy as np
import matplotlib.pyplot as plt
import sys

y0, theta, v0 = [float(e) for e in sys.argv[1:]]
g = 9.81

a = - 1 / (2 * v0**2) * g / np.cos(theta)**2
b = np.tan(theta)
c = y0

x1 = (-b + np.sqrt(b**2 - 4 * a * c))/ (2 * a)
x2 = (-b - np.sqrt(b**2 - 4 * a * c))/ (2 * a)

x_max = max(x1, x2)

x = np.linspace(0, x_max, 101)
y = a * x**2 + b * x + c

plt.plot(x,y)
plt.show()