First slide

Rectilinear Motion

Question

A body is dropped from the top of the tower covers a distance 7h in the last second if its journey, where ‘h’ is the distance covered in the first second. How much time does it take to reach the ground?

Easy

A

6s
B

4s
C

5s
D

3s

Solution

Let ‘n’ be the last second of its fall then $s_{n} = g (n - \frac{1}{2}) .......... (i)$
The distance travelled by a freely falling body in the last sec is
$\begin{array}{l} But h = \frac{1}{2} g t^{2} \\ = \frac{1}{2} g (1)^{2} = \frac{g}{2} \dots \dots \dots . . (i) \\ ∴ from (i) 7 h = g (n - \frac{1}{2}) \\ \Rightarrow 7 \frac{g}{2} = \frac{g}{2} (2 n - 1) \\ \Rightarrow 2 n - 1 = 7 \\ \Rightarrow n = 4 s \end{array}$
$∴$ The time taken to reach the ground is 4s

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