Explanation

(d) Given, $x = 0.20\ m,\ \ y = 0.20\ m,\ u = 1.8{ms}^{- 1}$
Let the ball strike the $n$th step of stairs,
$Vertical\ distance\ travelled$
$= ny = n \times 0.20 = \frac{1}{2}gt^{2}$
$Horizontal\ distance\ travelled,\ nx = ut$
$or\ \ t = \frac{nx}{u}$
$\therefore ny = \frac{1}{2}g \times \frac{n^{2}x^{2}}{u^{2}}$
$or\ n = \frac{2u^{2}}{g}\frac{y}{x^{2}} = \frac{2 \times (1.8)^{2} \times 0.20}{9.8 \times (0.20)^{2}}$
$= 3.3 = 4\ $