Question

A ball rolls horizontally off the top of a stairway with a speed of $1.5{\text{ms}}^{-1}$. The steps are $0.2\text{m}$ high and $0.2\text{m}$ wide. If the ball hits the edge of $n^{th}$ step first, then $n$ is
(Take $g=10m/s^2$)

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Total height through which the ball will fall down vertically before it strikes the $n^{th}$ step
$h=0.2\times n=0.2n$
Using second equation of motion, we get
$h=\frac{1}{2}g{t}^2$
$0.2n=\frac{1}{2}\times 10\times t^2$
$\begin{array}{}0.2n=5t^2& \text{(1)}\end{array}$
Horizontal distance travelled by the ball before striking the $n^{th}$ step
$R=0.2\times n=0.2n$
Now, $0.2n=u_x\times t$
$\begin{array}{}\Rightarrow 0.2n=1.5\times t& \text{(2)}\end{array}$
Solving $\left(1\right)$ and $\left(2\right)$, we get $n=2.25$
$\therefore$ Ball will first hit the 3rd step first