A tennis ball with (small) mass `m_(2)` rests on the top of a basketball of mass `m_(1)`which is at a height `h` above the ground, and the bottom of the tennis ball is at height `h+ d` above the ground. The balls are dropped. To what height does the tennis ball bounce with respect to ground? (Assume all collisions to be elastic and `m_(1)gt gt m_(2))`

Answer

`d+9h`

Explanation

Just before collision speed of any ball,
`v=sqrt(2gh)`
Just after collision `m_(1)` moves up with v while `m_(2)` moves down with `v`.
After the collision `e=(v'-v)/(v-(-v))=1`

`implies v'=3v`
`0^(2)=(3v)^(2)-2gh'`
`implies h'=(9v^(2))/(2g)impliesH=d+(9v^(2))/(2g)=d+9h`