A ball rolls off top of a staircase with a horizontal velocity `u m s^-1`. If the steps are `h` metre high and `b` mere wide, the ball will just hit the edge of `n th` step. Find the value of `n`.

Options

A. `n=(2hu)/(gb^(2))`
B. `n=(2hu^(2))/(gb)`
C. `n=(2hu^(2))/(gb^(2))`
D. `n=(hu^(2))/(gb^(2))`

Answer

C

Explanation

If the ball hits the nth step, then horizontal distance traversed=nh
Here, velocity along horizontal direction =u. velocity along vertical direction=0.

`:. nb=ut........(i)`
`nh=0+1/2"gt"^(2).......(ii)`
From (i), `t=(nb)/v, :. nh=1/2gxx((nb)/u)^(2)`
`n=(2hu^(2))/(gb^(2))`