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