A body is projected vertically upwards. If $a$ and $b$ be the times at which it is at height $h$ above the point of projection while ascending and descending respectively, then $h$ is :

(Take $g=10m/s^2$)

The correct option is A $5ab$
If the body is projected vertically upwards with a velocity $u$ ,

$h=ut-\frac{1}{2}g{t}^2$ (using formula $S=ut+\frac{1}{2}a{t}^2$)

or $t^2-\left(2u/g\right)t+2h/g=0$

This is a quadratic equation of $t$ and it has two roots $t_1=a$ and $t=b$ (say)

We know that, product of roots $=$ constant term/coefficient of $t^2$

So, $ab=\left(2h/g\right)/1$ or $h=gab/2$