First slide

Rectilinear Motion

Question

A body dropped from the top of a tower hits the ground after 4 s. How much time does it take to cover the first half of the distance from the top of the tower?

Moderate

A

1 s
B

2 s
C

$2 \sqrt{2} s$
D

$\sqrt{3} s$

Solution

Let h be the height of the tower. Then $h = \frac{1}{2} {gt}^{2} = \frac{1}{2} g (4)^{2} = 8 g$ .
The time taken to fall through $\frac{h}{2} = 4 g$ is given by $\frac{h}{2} = \frac{1}{2} {gt}^{2} or 4 g = \frac{1}{2} {gt}^{2} or t^{2} = 8 or t = 2 \sqrt{2} s$ .

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