A ball falls undal gravity from a height of 10m with an initial downward velocity u. It collides with ground, loses halft its energy and then rises back to the same height. Find the initial velocity u.

Options

A. `sqrt(2 gh)`
B. `sqrt(gh)`
C. `sqrt(3 gh)`
D. `sqrt(2.5 gh)`

Answer

A

Explanation

Total energy at the time of throwing the ball
`= mgh + (1)/(2) mv_(0)^(2)`
Energy after collision with ground
`= (1)/(2) (mgh + (1)/(2) mv_(0)^(2))`
The ball again rises to height `h`
`:. (1)/(2) (mgh + (1)/(2) mv_(0)^(2))= mgh`
or `mgh + (1)/(2) = 2 mgh`
`(1)/(2) mv_(0)^(2) = mgh or v_(0) = sqrt(2 gh)`