A particle of mass `m` moving with velocity `v_(0)` collides with sphere of same mass at rest , as shown. If the surface of contact is smooth and the collision is elastic, find the velocities of particle and sphere after the collision.

Explanation

The particle and sphere will perpendicular after the collision.

By the momentum conservation:
x-ax is: `mv_(0) = mv_(1) cos theta + mv_(2) cos theta(90 - theta)`
`v_(0) = v_(1) cos theta + v_(2) sin theta` (i)
`y-ax is: mv_(1) sin theta - mv_(2) sin (90 - theta)`
`0 = v_(1) sin theta - v_(2) cos theta`
Solving (i) and (ii), `v_(1) = v_(0) cos theta , v_(2) = v_(0) sin theta`
`cos theta = (1)/(2) , sin theta = (sqrt(3))/(2)`
`v_(1) = (v_(0))/(2) , v_(2) = (sqrt(3) v_(0))/(2)`