"""
Exercise 5.13 from "A primer on...
Animate the trajectory of a ball. We should plot the
curve for y(x) > 0, so we first need to solve
y(x) = 0 to find the upper bound for x. The 
formula is quadratic, so we solve a second-order
equation with the regular abc-formula. 
"""

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

y0 = float(sys.argv[1])
theta = float(sys.argv[2])
v0 = float(sys.argv[3])

g = 9.81

a = -g / (2 * v0**2 * 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)

#Use the largest of the two solutions (the positive one):
x_stop = max(x1, x2)

#create the x array, compute y, and plot the function:
x = np.linspace(0, x_stop, 101)
y = a * x**2 + b * x + c
plt.plot(x, y)
plt.show()