Question

A ball rolls off the top of stair-way with a horizontal velocity of magnitude $1.8 \, m \, s^{- 1}.$ The steps are $0.20 \, \, \text{m}$ high and $0.20 \, \, \text{m}$ wide. Which step will the ball hit first?

• A. First
• B. Second
• C. Third
• D. Fourth

Answer 1

Answer: (D)

Given, $x=0.20 \, m, \, y=0.20 \, m, \, u=1.8 \, m \, s^{- 1}$
Let the ball strike the $n$ th step of stairs,
Vertical distance travelled $= \, \, \text{n} \text{y}$
Using equation of motion in y-direction
$s=ut+\frac{1}{2}at^{2}$
$⟹-ny=0-\frac{1}{2}gt^{2}$ ...(1)
Horizontal distance travelled $= \, \, n x$
$\Longrightarrow \text{n}\text{x}=ut$
$\Longrightarrow t=\frac{n x}{u}$ ...(2)
using (1) and (2)
$ny=\frac{1}{2}g\left(\frac{n x}{u}\right)^{2}$
$or \, n=\frac{2 u^{2}}{g}\frac{y}{x^{2}}$ $=3.3\Longrightarrow 4^{t h} \, stair$