Question

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?

Answer 1

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

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

so,we have a projectile projected from height `0.2n` horizontally with velocity `4.5 ms^-1` and its range of motion is `0.3n`

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

`0.2n=1/2g t^2`

Given `g=10ms^-1`

so,`t=sqrt((0.4n)/10)`

And,along horizontal direction, using `R=vt`,we can write

`0.3n=4.5 t`

so,`0.3n/4.5 = sqrt(0.04n)` (putting the value of `t`)

or,`n^2/225 =0.04n`

so,`n=9`