from math import *

R = 10.0
v = 0.2
u = 0.25
h = 0.001
t = 0

b_x = b_y = 0

m_x = R
m_y = 0

def mother_pos(t):
   return (R*cos(v*t/R),R*sin(v*t/R))
   
while (b_x**2 + b_y**2) < R**2:
   mag = sqrt((m_x-b_x)**2 + (m_y - b_y)**2)
   db_x = u*(m_x - b_x)/mag
   db_y = u*(m_y - b_y)/mag
   
   b_x += db_x*h
   b_y += db_y*h
   
   
   (m_x,m_y) = mother_pos(t)
   t += h
   
print t