Question

A ball rolls off the top of a stairway horizontally with a velocity of ${4.5ms}^{-1}$. Each steps is $0.2m$ high and $0.3m$ wide. If $g$ is ${10ms}^{-2}$, and the ball strikes the edge of the $nth$ step, then $n$ is equal to:

• A. $9$
• B. $10$
• C. $11$
• D. $12$

Answer 1

The correct option is A $9$

It strikes on $n^{th}$ step edge.

Therefore, $4.5t=0.3n$

$\Rightarrow t=\frac{n}{15}$

$\frac{1}{2}{gt}^2=0.2n$

$\frac{1}{2}\times 10\times \frac{n^2}{{15}^2}=0.2n$

$\Rightarrow n=9$