A ball falls under gravity from a height of 10m with an initial downward velocity u. It collides with the ground, loses 50% of its energy in collision and then rises back to the same height. Find the initial velocity ''u''.

Explanation

`{:("Total initial"),("energy"):}}=(1)/(2)m u^(2)+mgh`
`{:("Energy after"),("collision"):}}=50%" of "((1)/(2)m u^(2)+mgh)`
`=(1)/(2)((1)/(2)m u^(2)+mgh)`
As the ball rebounds to same height,
`(1)/(2)((1)/(2)m u^(2)+mgh)=mgh`
`(1)/(2)((1)/(2)m u^(2)+mgh)=mgh`
`u=sqrt(2gh)`
`=sqrt(2xx9.8xx10)`
`=sqrt(196)`
initial velocity `u=14m//s`