Q. A ball rolls off the top of a stairway with horizontal velocity $v_{0}ms^{- 1}$. If the steps are $h$ metre high and $w$ metre wide, the ball will hit the edge of $n$th step if
A) $n = \frac{2hv_{0}}{gw^{2}}$
B) $n = \frac{2hv_{0}^{2}}{gw}$
C) $n = \frac{hv_{0}^{2}}{gw^{2}}$
D) $n = \frac{2hv_{0}^{2}}{gw^{2}}$
Explanation
(d) For horizontal motion,
$nw = v_{0}t\ \ or\ \ t = \frac{nw}{v_{0}}$
For vertical motion, $nh = \frac{1}{2}gt^{2}$
or $\frac{1}{2}g\left( \frac{n^{2}w^{2}}{v_{0}^{2}} \right) = nh\ \ \ or\ \ \ n = \frac{2hv_{0}^{2}}{gw^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.