Question

A ball rolls of the top of a stair way with a horizontal velocity $u\,m{{s}^{-1}}.$ If the steps are $h$ metre high and b metre wide, the ball will hit the edge of the nth step, where $n$ is

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

Answer 1

Answer: (B)

$\frac{2h{{u}^{2}}}{g{{b}^{2}}}$

Answer 2

Let the ball strike the, nth step after r second. Vertical distance travelled by ball $=nh=\frac{1}{2}g{{t}^{2}}.$ Horizontal distance travelled by ball $=nb=ut$ or $t=\frac{nb}{u}$ $nh=\frac{1}{2}g{{\left( \frac{nb}{u} \right)}^{2}}$ or $n=\frac{2{{u}^{2}}}{g}\frac{h}{{{b}^{2}}}$