Question
A body is dropped from height h (top of cliff) and at the same moment another particle is projected upwards from the ground. Both the bodies meet at a height h/n. Find the intial velocity of projection and show that, the velocities of two bodies when they meet are in the ratio (n-2):2(-1).
Solution
Ball A:
Initial position of ball, x0A = h
Initial velocity of ball, uA = 0
Acceleration, aA = -g
Therefore the position of the ball at any instant is, 
Ball B:
Initial position of ball, xOB = 0
Initial velocity of ball, uB = 0
Acceleration, aB = -g
Therefore, the position of the ball at any instant is,
xB = xOB + uBt + 
...(3)
When the balls meet, the position of both the balls is same.
XA = XB
h - 
... (2) 
Position at which the two balls meet,
x = xA = xB = h - 
But, x = 
Therefore, 
Velocity of balls, when they meet i.e., at t = h/u
