A ball is projected vertically down with an initial velocity from a height of 20 m on to a horizontal floor. During the impact it loses 50% of the energy and rebounds to the same height, the initial velocity of its projection is

Options

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

Answer

a

Explanation

From Equation of motion `v^(2)-u^(2) =2as`
`v^(2) =u^(2) +2gh" " v=sqrt(u^(2)+40g)` ` [h=20m] `
LOSS in energy =100-50=50%
`1/2`(initial energy)
`1/4mv_(2)=1/4mxx(u^(2)+40g)`
after ball rebound, remaining energy
`1/2mv^(2) =1/2m(2gh)`
` mgh=1/4m(u^(2)+40g)`
`u=sqrt(40g=sqrt(40xx10)=20m//s`
Negative sign negleccted since it indicates only direction]