Question

Single Correct Answer Type
A ball rolls of the top of a stair way with a horizontal velocity $u$ m/s. If the steps are $h$ metres high and $b$ metres wide, then ball will hit the edge of the $n^{th}$ step, if

• A. $n=\frac{2h{u}^2}{g{b}^2}$
• B. $n=\frac{2hu}{g{b}^2}$
• C. $n=\frac{2b^2}{2h{u}^2}$
• D. $n=\frac{g{b}^2}{2hu}$

Answer 1

The correct option is A $n=\frac{2h{u}^2}{g{b}^2}$

If the ball hits the $n^{th}$ step , then the height travelled by the ball is $=nh$
Range of the ball $=nb$
Using equations of motion ,
$nh=\frac{1}{2}g{t}^2$
$nb=ut$
$t=\frac{nb}{u}$
Substituting 't' in the equations of motion,
$nh=\frac{g{n}^2{b}^2}{2u^2}$
Thus the ball will hit the edge of the$n^{th}$ step, if$n=\frac{2h{u}^2}{g{b}^2}$