A ball rolls off top of a stair case with horizontal velocity `u (m)/(s)` if the steps are h meter high and b meter wide, the ball will just hit the edge of `n^(th)` step. Then value of n is:

Explanation

If the ball hits the `n^(th)` step, the horizontal and vertical distances traversed are nd and nh respectively. Let t be the time taken by the ball for these horizontal and vertical displacement. Velocity along horizontal direction =u (remains constant) and initial vertical velocity=zero.
`therefore nb=ut` and `nh=0+(1)/(2)"gt"^(2)`
Eliminating t from the equation
`nh=(1)/(2)g((nb)/(u))^(2) rArr n=(2hu^(2))/(gb^(2))`