question_answer

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

A) \[n=\frac{2hu}{g{{b}^{2}}}\] 

B)        \[n=\frac{2h{{u}^{2}}}{gb}\]

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

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

Correct Answer: C

Solution :

[c] If the ball hits the nth step, then the horizontal distance traversed = nh. Here, the velocity along the horizontal direction = u. Initial velocity along the vertical direction = 0.

So \[nb=ut\]                               ...(i)

\[nh=0+\frac{1}{2}g{{t}^{2}}\]                                   ...(ii).

From \[t=\frac{nb}{v},\] putting in eq. (ii)

\[nh=\frac{1}{2}g\times {{\left( \frac{nb}{u} \right)}^{2}}\] or \[n=\frac{2h{{u}^{2}}}{g{{b}^{2}}}\]