Motion In Two Dimensions Question 3
Question 3 - 2024 (29 Jan Shift 1)
A ball rolls off the top of a stairway with horizontal velocity $u$. The steps are $0.1 \mathrm{~m}$ high and $0.1 \mathrm{~m}$ wide. The minimum velocity $\mathrm{u}$ with which that ball just hits the step 5 of the stairway will be $\sqrt{\mathrm{x}} \mathrm{ms}^{-1}$ where $\mathrm{x}=$ [use $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$.
Show Answer
Answer: (2)
Solution:
The ball needs to just cross 4 steps to just hit $5^{\text {th }}$ step
Therefore, horizontal range $(\mathrm{R})=0.4 \mathrm{~m}$
$\mathrm{R}=$ u.t
Similarly, in vertical direction
$\mathrm{h}=\frac{1}{2} \mathrm{gt}^{2}$
$0.4=\frac{1}{2} \mathrm{gt}^{2}$
$0.4=\frac{1}{2} \mathrm{~g}\left(\frac{0.4}{\mathrm{u}}\right)^{2}$
$\mathrm{u}^{2}=2$
$\mathrm{u}=\sqrt{2} \mathrm{~m} / \mathrm{s}$
Therefore, $x=2$
