"""
Ex 5.13 from 'A primer on...'
We shall plot the trajectory of the ball, given
by y = f(x), for f(x)>0. To find the range of
x-values satisfying f(x) > 0 we solve the
equation f(x) = 0, which is a standard quadratic equation. 
"""


import sys
import numpy as np
import matplotlib.pyplot as plt
from math import tan, cos, sqrt

#unpack arguments and convert to float in one line:
y0, theta, v0 = [float(e) for e in sys.argv[1:]]
g = 9.81

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

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

#pick the largest root as the end point for x:
max_x = max(x1, x2)

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

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

"""Terminal> python plot_trajectory.py 2 0.8 4
(output is a plot)
"""