#exer 5.13
import sys
import numpy as np
from matplotlib.pyplot import *
from math import tan, cos,sqrt

def f(x,y0, theta, v0,g):
    return x * tan(theta) - (1/(2*v0**2))*((g*x**2)/(cos(theta)**2)) + y0

#read arguments from command line
y0 = float(sys.argv[1])
theta = float(sys.argv[2])
v0 = float(sys.argv[3])
g = 9.81

#solve equation to determine the x interval
a = - (1/(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)

#initialize and create the plot
x = np.linspace(0,x_max,100)
y = f(x,y0,theta,v0,g)

plot(x,y)
show()

"""
Terminal> python plot_trajectory.py 0.5 0.7 2
(output is a plot)
"""