# A ball rolls off the top of a stairway with a velocity u. If the height of each step is h, the breadth is b and the ball hits the edge of nth steps, the find the value of n.

$\begin{array}{1 1}(A)\;2hu \\(B)\;\frac{2hu^2}{gb^2} \\(C)\;\frac{1}{2}hu\\(D)\;0 \end{array}$

Horizontal distance covered by ball =nb
Vertical distance covered by ball =nh
If the time taken to hit the edge of nth step is t, then
$nb= ut$
$nh= \large\frac{1}{2}$$gt^2 Eliminating t, we get, nh = \large\frac{1}{2}$$g \bigg(\large\frac{nb}{u}\bigg)^2$
$n= \large\frac{2hu^2}{gb^2}$
Hence B is the correct answer.