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.

A particle of mass m moving with velocity v_(0) collides with sphere o

1.	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.
Answer» SOLUTION :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)`