A ball rolls off the top of a stairway with a horizontal velocity of magnitude 150 cm/sec. The steps are 20 cm high and 20 cm wide. Which step will the ball hit first?

A ball rolls off the top of a stairway with a horizontal velocity of m

1.	A ball rolls off the top of a stairway with a horizontal velocity of magnitude 150 cm/sec. The steps are 20 cm high and 20 cm wide. Which step will the ball hit first?
Answer» Solution :Let x be the horizontal distance measured from the foot of the edge of the step, the BALL leaves the TOP of stairway to the point it hits the nth step. `x=v_(0)t=1.5t`. …………….i where `v_(0)` is the initial horizontal SPEED. The height of the ball drops through is `y=nH=0.2n`..........ii Where n is the NUMER of steps and H=20cm is the height of each step. As the vertical component of initial velocity is zero, the vertical distance TRAVERSED in the same time t is `y=1/2"gt"^(2)`........iii and `x=nw=0.2`n.......iv `x=y=0.2n`........iv `V_(0)t=1/2"gt"^(2),t=(2V_(0))/g=(2xx150xx10^(-2))/10` `impliest=0.3s` `:.0.2n=1.5(0.3)impliesn=2.25m:.n=3`