Question

A ball rolls off the top of a stairway horizontally with a velocity of $5\text{m/s}$. Each step is $0.1\text{m}$ high and $0.1\text{m}$ wide. If $g=10{\text{m/s}}^2$ and the ball strikes the $n^{th}$ step, then find the value of $n$.

• A. $50$
• B. $10$
• C. $110$
• D. $12$

Answer 1

The correct option is A $50$


When the ball strikes $n^{th}$ step, then horizontal displacement:
$X=w\times n=0.1n\text{m}$
where $w=$ width of each step

Similarly, vertical displacement :
$Y=h\times n=0.1n\text{m}$;
where $h=$ height of each step.

Now, time of flight when the ball strikes $n^{th}$ step:

$T=\sqrt{\frac{2Y}{g}}=\sqrt{\frac{2\times 0.1n}{g}}...\left(i\right)$
Equation for horizontal range:-
$X=v\times T....\left(ii\right)$

$\therefore 0.1n=5\times \sqrt{\frac{0.2n}{10}}$
$\Rightarrow n=\frac{25\times 0.2}{{0.1}^2\times 10}=50$