Question

A ball rolls off the top of a stairway with horizontal velocity v0 m/s. If the steps are h metres high and w metres wide, the ball will hit the edge of $n^{th}$ step, if:

• A. $n=\frac{2h{v}_0}{g{w}^2}$
  
• B. $n=\frac{2h{v}_0^2}{gw}$
  
• C. $n=\frac{hv{62}_0}{g{w}^2}$
  
• D. $n=\frac{2h{v}_0^2}{g{w}^2}$

Answer 1

The correct option is D $n=\frac{2h{v}_0^2}{g{w}^2}$


$y=nh=ut+\frac{1}{2}g{t}^2$
Since ball is released u = 0
$y=nh=\frac{1}{2}g{t}^2.....\left(i\right)$
x = Range = nw = $(velocity{)}_{Horizontal}\times time$ of flight
$x=nw=v_0\times tt=\frac{nw}{v_0}.....\left(ii\right)$
By (i)and (ii)$n=\frac{2h{v}_0^2}{g{w}^2}$