__author__ = 'Lenovo'
import numpy as np

a = np.pi / 4
g = 9.8
v0 = 30
l1 = np.sin(2*a) * v0 ** 2 / g
print 'flight length in Galiley model:' + str(l1)


ro = 7600
r = 0.2
u = v0 * np.cos(a)
w = v0 * np.sin(a)
h = 0.01
b = 0.16 * 1.15 * np.pi * r * r / 2.0
m = ro * 4 * np.pi * r * r * r /3
x = 0
y = 0
f = False
xprev = 0
yprev = 0

def deriv_u_t(u, w):
    return (-b) * u * np.sqrt(u**2 + w**2) / m

def deriv_w_t(u, w):
    return -g - b * w * np.sqrt(u**2 + w**2) / m

while (True):
    k1u = h * deriv_u_t(u, w)
    k1w = h * deriv_w_t(u, w)
    k2u = h * deriv_u_t(u + h * k1u/2, w + h * k1w/2)
    k2w = h * deriv_w_t(u + h * k1u/2, w + h * k1w/2)
    k3u = h * deriv_u_t(u + h * k2u/2, w + h * k2w/2)
    k3w = h * deriv_w_t(u + h * k2u/2, w + h * k2w/2)
    k4u = h * deriv_u_t(u + h * k3u, w + h * k3w)
    k4w = h * deriv_w_t(u + h * k3u, w + h * k3w)
    u += (k1u + 2 * k2u + 2 * k3u + k4u)/6
    w += (k1w + 2 * k2w + 2 * k3w + k4w)/6

    v = np.sqrt(u**2 + w**2)

    xprev = x
    yprev = y

    x += u * h
    y += w * h

    if (y == 0):
        f = True
        break
    if (y < 0):
        break


print 'flight length in Newton model:'
if (f):
    print x
else:
    print (xprev * y - x * yprev) / (y - yprev)