A juggler throws balls into air. He throws one when ever the previous one is at its highest point. If he throws n balls each second, the height to which each ball will rise is:

The correct option is A $\frac{g}{2n^2}$

Juggler throws the ball into the air with ball having initial velocity $=u$

At the highest point of its path velocity will be zero as at maximum height velocity $=0$

So final velocity $v=0$

According to question juggler throws $n$ balls each second.

Time taken to reach highest position $t=\frac{1}{n}$

Using equation of the motion we get:-

$v=u+at$

$0=u-\frac{g}{n}$

$u=\frac{g}{n}$

Also,

Distance travelled in $t=\frac{1}{n}$ secs:-

$H=ut-\frac{g{t}^2}{2}$

$H=\frac{g}{n^2}-\frac{g}{2n^2}$

Required height to which each ball rise, $H=\frac{g}{2n^2}$