Question

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

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

Answer 1

The correct option is A $9$

Total height by 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 $h=u_y+\frac{1}{2}g{t}^2$
As $u_y=0$
$\Rightarrow 0.2n=\frac{1}{2}\times 10\times t^2=5t^2.......\left(i\right)$
Horizontal distance travelled by the ball before striking the $n^{th}$ step, $R=0.3\times n=0.3n$
Using second equation of motion, we get $R=u_{x}t+\frac{1}{2}{a}_x{t}^2$
As $a_x=0\Rightarrow 0.3n=4.5t.......\left(ii\right)$
Dividing $\left(i\right)$ by $\left(ii\right)$, we get $\frac{2}{3}=\frac{50}{45}t$ or $t=0.6\text{s}$
Now, $0.3n=4.5\times 0.6=2.7$ or $n=\frac{2.7}{0.3}=9$