Question

A small ball rolls of the top of a stairway horizontally with a velocity of $4.5m{s}^{-1}$. Each step is $0.2m$ high and $0.3$ m wide. If g is $10$ ms${}^{-2}$, then the ball will strike the $n^{th}$ step where $n$ is equal to (assume ball strike at the edge of the step)

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

Answer 1

Answer: (A)

$9$

$0.2n=\frac{1}{2}g{t}^2=\frac{1}{2}\times 10t^2=5t^2$

$0.3n=4.5t$

Dividing, $\frac{2}{3}=\frac{50}{45}t$

$t=0.6s$

Now, $0.3n=4.5\times 0.6=2.7$

$n=\frac{2.7}{0.3}=9$

So, the ball will strike the 9th step.
Hence, option A is correct.