"""
Ex 5.13 from A primer on...
"""

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

from math import cos, tan, sqrt

#the code needs exactly 3 command-line args
y0, theta, v0 = [float(arg) for arg in sys.argv[1:]]
g = 9.81

"""
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.
"""

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_max = max(x1,x2)
x = np.linspace(0,x_max,101)

#simple formula since a,b,c were defined above:
y = a*x**2 + b*x + c

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

"""
Terminal> python plot_trajectory.py 0.5 0.78 2.5
"""