A ball is thrown vertically down from a height of 40m from the ground with an initial velocity .v.. The ball hits the ground, loses one-third of its total mechanical energy and rebounds back to the same height. If the acceleration due to gravity is `10ms^(-2)`, the value of .v. is

Options

A. `5ms^(-1)`
B. `10ms^(-1)`
C. `15ms^(-1)`
D. `20ms^(-1)`.

Answer

D

Explanation

`h=40m`
Energy loss `=(1^nl)/(3)` of mechanical energy `g=10ms^(-2)`.
Total mechanical energy be `=1J`
Remaining energy `=1-(1)/(3)=(2)/(3) J`.
`(2)/(3)((1)/(2)mv^2+mgh)=mgh`
`rArr (2)/(3)((1)/(2)v^2+gh)=gh`
`rArr (1)/(3)v^2+(2)/(3)gh=gh`
`(v^2)/(3)=gh-(2)/(3)gh`
`rArr (v^2)/(3)=(3gh-2gh)/(3)`
`rArr (v^2)/(3)=(gh)/(3)`.
`v^2=gh`.
`v=sqrt(gh) rArr v=sqrt(400)rArr v=20 m //sec`/