A body projected vertically up with a velocity of 10 m $s^{-1}$ reaches a height of 20 m. If it is projected with a velocity of 20 m $s^{-1}$ then the maximum height reached by the body will be :

The correct option is C 80 m
Given , $v=0,u=10m/s,h=20m$ ,

By using ,

$v^2=u^2-2gh$

$0^2={10}^2-2g\times 20$

or $g=100/40=5/2m/s^2$

Now , if $v^{\prime }=0,u^{\prime }=20m/s,h^{\prime }=?,g=5/2m/s^2$ ,

Again by using ,

$v^2=u^2-2gh$

$0^2={20}^2-2\times \left(5/2\right)\times h^{\prime }$

or $h^{\prime }=400/5=80m$