"""
Ex 5.13 from A primer on...
"""
import sys
import numpy as np
import matplotlib.pyplot as plt

from math import cos, tan, sqrt

"""
We should plot for y=f(x)>0, so
we must solve a quadratic equation
a*x**2 +b*x + c = 0
to find the right range of x values.
"""

#Assume the arguments are given in the order y0, theta, v0
y0 = float(sys.argv[1])
theta = float(sys.argv[2])
v0 = float(sys.argv[3])
g = 9.81

a = -1.0/(2*v0**2)*g/(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)

x_stop = max(x1,x2)

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

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


"""
Terminal> python plot_trajectory.py 0.75 0.78 5
output is a plot
"""