First slide

Projection Under uniform Acceleration

Question

A ball rolls of the top of a stair way 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

$n = 2 hu / {gb}^{2}$
B

$n = 2 {hu}^{2} / {gb}^{2}$
C

$n = 2 {hu}^{2} / gb$
D

$n = {hu}^{2} / {gb}^{2}$

Solution

The situation is shown in fig. (1)
If the ball hits the ns step, then
horizontal distance traversed = nb
vertical distance traversed = nh
Here, velocity along horizontal direction = u
velocity along vertical direction = 0
$\begin{array}{l} ∴ nb = ut and nh = 0 + \frac{1}{2} {gt}^{2} \\ or t = \frac{nb}{u} and nh = \frac{1}{2} g \times {(\frac{nb}{u})}^{2} \\ ∴ n = \frac{2 {hu}^{2}}{{gb}^{2}} \end{array}$

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