"""
Exercise 5.13
This is a standard plotting exercise, except
for the requirement to plot y=f(x), for y >=0.
This means we need to find the x-interval where
y>=0, and use this to construct our x array.
Since f(x) is quadratic in x, we can solve it
with the standard formula.
"""

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

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

"""
First solve f(x) = 0, using the standard formula,
since f is on the form a*x**2 + b*x + c = 0
"""
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)

#choose the largest (the other should be negative)
x_max = max(x1,x2)

#now we know the x range and can make the array
x = np.linspace(0,x_max,101)

#evaluate formula using a,b,c, since we defined these above:
y = a*x**2 + b*x +c

plt.plot(x,y)

#decorate the plot
plt.xlabel('distance (m)')
plt.ylabel('height (m)')
plt.title('Trajectory of a ball')

plt.show()

"""
Terminal> python plot_trajectory.py 1 0.78 5
(output is a plot)
"""