Two smooth balls A and B, each of mass m and radius R, have their centre at (0,0,R) and (5R,-R,R) respectively, in a coordinate system as shown. Ball A, moving along positive x-axis, collides with ball B. Just before the collision, speed of ball A is 4m/s and ball B is stationary. The collision between the balls is elastic. Velocity of the ball A just after the collsion is

Explanation

(a) As the collision is elasties & bodies are of equal mass, the velocity along the line of collision will interchange. As no force acts perpendicular to line of impact, therefore velocity of `A` perpendicular to the line of impact (4 sin 30) will remain same.

from the figure it is clear that velocity of `A` is `4 sin 30` and velocity of `B` is `4 cos 30` and both move at `90^(@)` to each other.
(b) `vecJ_("AonB")=m(vecv_(Bf)-vecv_(Bi))`
`m[4cos30^(@)(cos30^(@)hati-sin30^(@)hatj)-0]`
`(3mhat"i"-sqrt3mhat"j")kg-m//s`
Impulse of collision is always along the line of collision.