Prove that time taken by a body to rise to highest point is always equal to the time taken by it to fall through he same height.

Explanation

(i) Time taken by body to rise to highes point
from `v=v+at`
`0=u-g t, t=(u)/(g)`
From `v^(2)-u(2)=2as`
`0-u^(2)=(-g)h,h=u^(2)/2g`
this is the maximum height.
(ii) time taken by the bnody to fall to ground
From `s=ut+(1)/(2)at^(2)`
`u^(2)/2g=0+(1)/(2)g t^(2)`
`r^(2)=u^(2)/g^(2),t=(u)/(g)` which is same as in (i) above.