Q. A tennis ball rolls off the top of a stair case way with a horizontal velocity $u\ ms^{- 1}$. If the steps are $b$ metre wide and $h$ metre high, the ball will hit the edge of the $n$th step, if
A) $n = \frac{2hu}{gb^{2}}$
B) $n = \frac{2hu^{2}}{gb^{2}}$
C) $n = \frac{2hu^{2}}{gb^{\ }}$
D) $n = \frac{hu^{2}}{gb^{2}}$
Explanation
(b) $nh = \frac{1}{2}gt^{2}\ \Rightarrow t = \sqrt{\left( \frac{2nh}{g} \right)}$ …(i)
Horizontal distance travelled by ball
$nb = ut,nb = u\sqrt{\left( \frac{2nh}{g} \right)}$ ….(ii)
Squaring Eq. (ii), we get
$n^{2}b^{2} = \frac{u^{2}2nh}{g}$
$\therefore n = \frac{2u^{2}h}{gb^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.