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A fish rising vertically up towards the surface of water with speed 3 ms^–1 observes a bird diving vertically down towards it with speed 9 ms^–1. The actual velocity of bird is (refractive index of water is 4/3)

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3.0 ms^–1

4.5 ms^–1

3.4 ms^–1

5 ms^–1

answer is A.

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Detailed Solution

Velocity of the bird with respect to stationary fish

$v_{BF} = {μv}_{B} where v_{B} is the actual velocity of the bird$

$Relative velocity of the bird w . r . t moving fish$

$v_{F} + {μv}_{B} = 9 (given)$

$3 + \frac{4}{3} v_{B} = 9$

$v_{B} = 4.5 m / s$

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