Question

A ball is projected vertically down with an initial velocity from a height of `20 m` onto a horizontal floor. During the impact it loses `50%` of its energy and rebounds to the same height. The initial velocity of its projection is
A. `20 ms^(-1)`
B. `15 ms^(-1)`
C. `10 ms^(-1)`
D. `5 ms^(-1)`

Answer 1

Correct Answer - A
Let ball is projected vertically downwards with velocity `v` from height `h`
Total energy at point `A + (1)/(2) mv^(2) + mgh`

During collision loss of energy is `50%` and the ball rises up to same height . It posses only potential energy at same level.
`50% ((1)/(2) mv^(2) + mgh) = mgh`
`(1)/(2) ((1)/(2) mv^(2) + mgh) = mgh`
`v = sqrt(2 gh) = sqrt(2 xx 10 xx 20)`
`:. v= 20 m//s`