A spherical imperfectly elastic ball strikes a plane with velocity `8 m//s` at an angle of `30^(@)` with the plane. Determine the magnitude and direction of the velocity after impact if `e = 0.5` (neglect gravity).

Explanation

Resolving the velocity before impact, velocity component along the plane `=8sin60^(@)=4sqrt(3) m//s` and that normal to the plane =`8cos60^(@)=4m//s`.
If `v m//s` is the velocity after the impact and `theta` the angle made by the velocity with the normal to the plane, then velocity component along the plane `=vsintheta` and that normal to the plane `=v costheta`.
As the velocity along the plane remains uchanged,
`:. vsintheta=4sqrt(3)`.............i
Fom Newton's expereimental law,
`costheta=e(4)` (in magnitude)
`=2 `................ii
squaring and adding eqn i and ii
`v^(2)=52impliesv=2sqrt(13)m//s`
`dividing eqn i by eqn ii we get