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Q.

A body freely falling from a height h describes 7h/16 in the last second of its fall. The height h is (g = 10 ms^–2).

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a

40 m

b

160 m

c

45 m

d

80 m

answer is A.

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Detailed Solution

$S_{n} = u + \frac{1}{2} g (2 n - 1) \Rightarrow \frac{7 h}{16} = \frac{1}{2} g (2 n - 1) B u t h = \frac{1}{2} g t^{2} = \frac{1}{2} g n^{2} ∴ \frac{7}{16} \times \frac{1}{2} g n^{2} = \frac{1}{2} g (2 n - 1) n = 4 ∴ h = \frac{1}{2} g n^{2} = \frac{1}{2} \times 10 \times 4^{2} = \frac{10 \times 16}{2} = 80 m$

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