First slide

Projection Under uniform Acceleration

Question

A ball rolls off the top of a staircase with a horizontal velocity u ms^-1. If the steps are h metre high and b metre wide, the ball will hit the edge of the nth step, if

Moderate

A

$n = \frac{2 hu}{{gb}^{2}}$
B

$n = \frac{2 {hu}^{2}}{gb}$
C

$n = \frac{2 {hu}^{2}}{{gb}^{2}}$
D

$n = \frac{{hu}^{2}}{{gb}^{2}}$

Solution

If the ball hits the nth step, then horizontal distance traversed = nh. Here, velocity along horizontal direction $= u \cdot n = ut$ Initial velocity along vertical direction is 0.

$nh = 0 + \frac{1}{2} {gt}^{2} ∣ From t = \frac{nb}{v}, putting t in (ii), we get nh = \frac{1}{2} g \times {(\frac{nb}{u})}^{2} or n = \frac{2 {hu}^{2}}{{gb}^{2}}$

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