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A ball rolls off the top of a stariway w...

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

Text Solution

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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`
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