question_answer

A ball rolls off 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 nth step, if

A)  \[n=\frac{2h{{u}^{2}}}{g{{b}^{2}}}\]        

B)         \[n=\frac{2hu}{g{{b}^{2}}}\]

C)  \[n=\frac{2{{b}^{2}}}{2h{{u}^{2}}}\]      

D)         \[n=\frac{g{{b}^{2}}}{2hu}\]

Correct Answer: A

Solution :

 If the ball hits \[nth\] step, then horizontal distance traversed\[=nb\] vertical distance traversed\[=nh\] Here velocity along vertical direction\[=0\] \[\therefore \]      \[nb=ut\],          and       \[nh=0+\frac{1}{2}g{{t}^{2}}\] \[\Rightarrow \]   \[t=\frac{nb}{u}\],         and       \[nh=\frac{1}{2}g{{\left( \frac{nb}{u} \right)}^{2}}\]