A Juggler throws balls into air. He throws one whenever the previous is at its highest point. If he throws $n$ balls each second, the height to which each balls will rise is

The correct option is A $\frac{g}{2n^2}$
Time taken by each ball to reach max height is
$t=\frac{1}{n}$
At maximum height, $v=0$
So, from first equation of motion
$v=u+at$
$\Rightarrow 0=u–g\frac{1}{n}$
$\Rightarrow u=\frac{g}{n}$
Also, from third equation of motion, we get
$v^2=u^2+2a{H}_{max}$
$\Rightarrow 0=\frac{g^2}{n^2}-2g{H}_{max}$
$\Rightarrow H_{max}=\frac{g}{2n^2}$
Hence, the height to which each balls will rise is
$H_{max}=\frac{g}{2n^2}$