A ball rolls off top of a stair way with horizontal velocity $u\; m/s$ If height of each step is h and width of each step is b the ball will hit the edge of $n^{th}$ step if $n$ is equal to

Question

                               

Answer 1

If the ball hits the $n^{th}$ step vertical distance travelled in $nh$ horizontal distance travelled is $nb$

Let $t$ be the time of fall

Initaial vertical velocity $=0$

Therefore $nb=ut$----(1)

$nh=0+\large\frac{1}{2}$$gt^2$-----(2)

from (1) and (2)

$n= \large\frac{2hu^2}{gb^2}$

Hence d is the correct answer.