"""
Exercise 5.11
This is the same as 5.10, but we will also compute
the max values of t and y, and use these to set the
size of the axes. The axes are normally set automatically
by matplotlib, but in some cases (for instance animation)
it is better to set them manually.
"""
import numpy as np
import matplotlib.pyplot as plt
import sys

v0_list = [float(v) for v in sys.argv[1:]]
g = 9.81

#the largest t occurs for the largest v0:
v0_max = max(v0_list)
t_max = 2*v0_max/g

"""
Thinking like a physicist, one may see from the
parabolic shape of the formula that the highest y
value will occur for the highest v0 value and for
t = v0/g (the midpoint).
Therefore, max_y = v0_max*t-0.5*g*t**2,
with t = v0_max/g.
However, we will think like programmers, and
use another approach to find y_max:
"""

y_max = 0 #choose a value we know is < the true max

for v0 in v0_list:
    t_stop = 2*v0/g
    t = np.linspace(0,t_stop,101)
    y = v0*t -0.5*g*t**2
    if max(y) > y_max:
        y_max = max(y) #update y_max if we found a higher value
    plt.plot(t,y,label='v0 = %g' %(v0))

plt.xlabel('time (s)')
plt.ylabel('height (m)')
plt.title('Height of ball')
plt.axis([0,t_max,0,y_max*1.1])
plt.grid()
plt.legend()

plt.show()

"""
Terminal> python plot_ball3.py 5 10 15
(output is a plot)
"""