First slide

Projection Under uniform Acceleration

Question

A ball rolls off the top of a staircase with a horizontal velocity u m/s. 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.
Velocity along vertical direction = 0.
$∴ nb = ut$ -----------------(i)
$nh = 0 + \frac{1}{2} {gt}^{2}$ -----------(ii)
From (i), $t = \frac{nb}{v}, ∴ = nh = \frac{1}{2} g \times {(\frac{nb}{u})}^{2}$
$n = \frac{2 {hu}^{2}}{{gb}^{2}}$

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