First slide

Position Path Length (Distance) And Displacement

Question

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

Moderate

A

3 sec
B

4 sec
C

5 sec
D

6 sec

Solution

Using the formula v² = u² + 2 g h, we have
$0 = u^{2} - 2 gh or u^{2} = 2 gh$
$0 = (2 u)^{2} - 2 gH or 4 u^{2} = 2 gH$
$\begin{array}{ll} ∴ \frac{h}{H} = \frac{1}{4} or 4 h = H \\ s_{n} = \frac{1}{2} g (2 n - 1) \\ or 7 h = \frac{1}{2} g (2 n - 1) . . . . (1) \\ and h = \frac{1}{2} g (2 - 1) or h = \frac{g}{2} . . . (2) \end{array}$
From eqs. (1) and (2), we get
$7 \times \frac{g}{2} = \frac{1}{2} g (2 n - 1)$
or 7=(2n-1) or n=4
hence t = 4sec

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