First slide

Projectile motion

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

$n = \frac{2 h u}{g b^{2}}$
B

$n = \frac{2 h u^{2}}{g b}$
C

$n = \frac{2 h u^{2}}{g b^{2}}$
D

$n = \frac{h u^{2}}{g b^{2}}$

Solution

If the ball hits the n^th step, then horizontal distance traversed = nh. Here, velocity along horizontal
direction = u.n = ut …….(i)
Initial velocity along vertical direction is 0.
$n h = 0 + \frac{1}{2} g t^{2}$ …..(ii)
$From t = \frac{n b}{v}, putting t in (ii), we get$
$n h = \frac{1}{2} g \times {(\frac{n b}{u})}^{2} or n = \frac{2 h u^{2}}{g b^{2}}$

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