Angry birds trajectory

angry.py

"""
Angry birds trajectory calculation and plotting
"""
import numpy as np
import pylab as pl

#### Input parameters
Y = 2
X = 55
g = 10
tmax = 2.5
####

def trajectory(v, a, g, tf):
    """
    Return a trajectory with these parameters
    v: starting velocity
    a: starting angle (radian)
    g: the gravitational constant
    tf: final time
    """
    t = np.linspace(0, tf, 100)
    x = v * np.cos(a) * t
    y = v * np.sin(a) * t - 0.5 * g * t**2
    return x, y

## Calculate and plot things
alpha = np.arctan((Y + 0.5*g*tmax**2)/X)
v0 = X/(tmax * np.cos(alpha))
print "Starting angle: %f rad / %f deg" %(alpha, alpha/np.pi*180)
print "Starting velocity: %f m/s" %(v0)

xpos, ypos = trajectory(v0, alpha, g, tmax)
pl.plot(X, Y, 'go', markersize=10, label="Pig") # Target to hit
pl.plot(xpos, ypos, 'r-', linewidth=2, label="An angry bird") # trajectory
pl.legend(loc='best', numpoints=1)
pl.xlabel('Distance (m)')
pl.ylabel('Height (m)')
pl.show()