Kinematics Question 625
Question: A ball rolls off to the top of a staircase with a horizontal velocity u m/s. If the steps are h meter high and b meter wide, the ball will hit the edge of the nth step, if
Options:
A) $ n=\frac{2hu}{gb^{2}} $
B)$ n=\frac{2hu^{2}}{gb} $
C) $ n=\frac{2hu^{2}}{gb^{2}} $
D)$ n=\frac{hu^{2}}{gb^{2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] If the ball his the nth step, then the horizontal distance traversed = nh.
Here, the velocity along the horizontal direction = u. Initial velocity along the vertical direction = 0.
So $ nb=ut $ …(i)
$ nh=0+\frac{1}{2}gt^{2} $ …(ii).
From $ t=\frac{nb}{v}, $ putting in eq. (ii)
$ nh=\frac{1}{2}g\times {{( \frac{nb}{u} )}^{2}} $ or $ n=\frac{2hu^{2}}{gb^{2}} $
