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#