Question

A ball rolls off the top of stair-way with a horizontal velocity of magnitude $1.8m{s}^{-1}.$ 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, $x=0.20m,y=0.20m,u=1.8m{s}^{-1}$
Let the ball strike the $n$ th step of stairs,
Vertical distance travelled $=\text{n}\text{y}$
Using equation of motion in y-direction
$s=ut+\frac{1}{2}a{t}^2$
$⟹-ny=0-\frac{1}{2}g{t}^2$ ...(1)
Horizontal distance travelled $=nx$
$⟹\text{n}\text{x}=ut$
$⟹t=\frac{nx}{u}$ ...(2)
using (1) and (2)
$ny=\frac{1}{2}g{\left(\frac{nx}{u}\right)}^2$
$orn=\frac{2u^2}{g}\frac{y}{x^2}$ $=3.3⟹4^{th}stair$