# A ball rolls off the top of Stairway horizontally with a velocity of 4.5 M per second each step is 0.2 M and 0.3 M wide if she is 10 M per second square then the ball will strike the end step Where n is equal to?

Mar 17, 2018

Considering that here $n$ stands for the number of stairs covered during hitting the stairs.

So,height of $n$ stairs will be $0.2 n$ and horizontal length $0.3 n$

so,we have a projectile projected from height $0.2 n$ horizontally with velocity $4.5 m {s}^{-} 1$ and its range of motion is $0.3 n$

So,we can say if it took time $t$ to reach the end of $n$ th stair,then considering vertical motion,using $s = \frac{1}{2} g {t}^{2}$ we get,

$0.2 n = \frac{1}{2} g {t}^{2}$

Given $g = 10 m {s}^{-} 1$

so,$t = \sqrt{\frac{0.4 n}{10}}$

And,along horizontal direction, using $R = v t$,we can write

$0.3 n = 4.5 t$

so,$0.3 \frac{n}{4.5} = \sqrt{0.04 n}$ (putting the value of $t$)

or,${n}^{2} / 225 = 0.04 n$

so,$n = 9$