A ball rolls off the top of a staircase with a horizontal velocity u m/s. If the steps are h metre high and b metre wide, the ball will hit the edge of the nth step, if

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

$\therefore \mathrm{nb}=\mathrm{ut}...\left(\mathrm{i}\right)$

$\mathrm{nh}=0+\frac{1}{2}{\mathrm{gt}}^2...\left(\mathrm{ii}\right)$
From eqn. (i),
$\begin{array}{l}\mathrm{t}=\frac{\mathrm{nb}}{\mathrm{u}},\therefore \mathrm{nh}=\frac{1}{2}\mathrm{g}{\left(\frac{\mathrm{nb}}{\mathrm{u}}\right)}^2\\ \therefore \mathrm{n}=\frac{2{\mathrm{hu}}^2}{{\mathrm{gb}}^2}\end{array}$