A small ball is dropped from rest from height 10 m on a horizontal floor. If coefficient of restitution between ground and body is `0.5` then find the maximum height it can rise after collision.

Explanation

The ballis dropped from height `h_(1)` so velocity just before hitting the ground= velocity of approach
`=V_("approach"=sqrt(2gh_(1)))`
The ball rises to the height `h_(2),` so velocity when just leaves the ground = velocity of sparation
`=sqrt(2gh_(2))=V_("separation")`
Coefficient of restitution,
`e=(V_("separation"))/(V_("approach"))`
`impliese=sqrt((2gh_(2))/(2gh_(1)))=sqrt((h_(2))/(h_(1)))`
`impliesh_(2)=e^(2)h_(1)`
`=1/4xx10=2.5m`