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A body is projected vertically up with certain velocity. At a point 'P' in its path, the ratio of its potential to kinetic energies is 9 : 16. The ratio of velocity of projection to velocity at 'P' is,

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3 : 4

5 : 4

9 : 25

25 : 16

answer is B.

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Detailed Solution

$\frac{(P E)_{p}}{(K E)_{p}} = \frac{9}{16} \Rightarrow (P E)_{p} = \frac{9}{16} (K E)_{p}$

$Now (K E)_{p} + (P E)_{p} = (K E)_{i}$

$\Rightarrow (K E)_{p} + \frac{9}{16} (K E)_{p} = (K E)_{i}$

$\Rightarrow \frac{(K E)_{i}}{(K E)_{p}} = \frac{25}{16} \Rightarrow \frac{V_{i}^{2}}{V_{p}^{2}} = \frac{25}{16}$

$\frac{V_{i}}{V_{p}} = \frac{5}{4}$

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