question_answer

A ball rolls off the top of a stairway with horizontal velocity \[{{v}_{o}}\text{ }m/s.\]If the steps are h metres high and w metres wide, the ball will hit the edge of n111 step, if:

A) \[n=\frac{2h{{v}_{o}}}{g{{w}^{2}}}\]                      

B) \[n=\frac{2h{{v}^{2}}_{o}}{gw}\]

C) \[n=\frac{h{{v}^{2}}_{o}}{g{{w}^{2}}}\]                

D) \[n=\frac{2h{{v}^{2}}_{o}}{g{{w}^{2}}}\]

Correct Answer: D

Solution :

    \[y=nh=ut+\frac{1}{2}g{{t}^{2}}\] Since ball is released u=0 \[y=nh=\frac{1}{2}g{{t}^{2}}\]                                               (1) \[x=Range=nw={{(velocity)}_{Horizonrtal}}\times time\,\,of\] \[flight\] \[x=nw={{v}_{o}}\times t\] \[t=\frac{nw}{{{v}_{o}}}\]                                                       (2) \[By\,\,\,\left( 1 \right)\,\,\And \,\,\left( 2 \right)\,\,n=\frac{2h{{v}^{2}}_{0}}{g{{w}^{2}}}\]