A ball rolls off the top of a staircase with a horizontal velocity `u ms^-1`. If the steps are `h` metre high and `b` metre wide, the ball will hit the edge of the `nth` step, if.

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))`