Question

A ball rolls off the top of a staircase with velocity u m/s . If the steps are h metre high and b metre wide, the ball will hit the edge of nth step, when

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

Answer 1

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

If the ball hits the nth step, then vertical distance travelled = nh. Here, velocity along horizontal direction = u and distance travelled in horizontal direction is nb = ut.
$\Rightarrow t=\frac{nb}{u}$
. Initial velocity in vertical direction is $0$ and distance travelled in vertical direction will be given by $nh=\frac{g{t}^2}{2}$ .Putting value of t in above equation ,we get
$nh=\frac{g}{2}{\left(\frac{nb}{u}\right)}^2\Rightarrow n=\frac{2h{u}^2}{g{b}^2}$