Question

A ball rolls off the top of stair way with a horizontal velocity of magnitude $1.8\text{m/s}$. The steps are $0.2\text{m}$ high and $0.2\text{m}$ wide. Which step will the ball hit first?

• A. $\text{First}$
• B. $\text{Second}$
• C. $\text{Third}$
• D. $\text{Fourth}$

Answer 1

The correct option is D $\text{Fourth}$

Let the ball strike the $nth$ step of stairs.
$\therefore$Vertical distance travelled =$ny=n\times 0.2=\frac{1}{2}g{t}^2$
Horizontal distance travelled$=nx=ut$
$\Rightarrow t=\frac{nx}{u}$
$ny=\frac{1}{2}g{t}^2=\frac{1}{2}g{\left(\frac{nx}{u}\right)}^2=\frac{1}{2}g\frac{n^2{x}^2}{u^2}$
$\Rightarrow n=\frac{2u^{2}y}{g{x}^2}=\frac{2\times {1.8}^2\times 0.2}{9.8\times {0.2}^2}\approx 3.3$
So, Fourth step.