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?

1 Answer
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 0.2n 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