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Q.

A fish rising vertically to the surface of water in a lake uniformly at the rate of $3 {ms}^{- 1}$ observes a bird diving vertically towards the water at a rate of $9 {ms}^{- 1}$ vertically above it. If the refractive index of water is $4/3$ , the actual velocity of the dive of the bird

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a

6 {ms}^{- 1}

b

2 {ms}^{- 1}

c

4.5 {ms}^{- 1}

d

1.5 {ms}^{- 1}

answer is B.

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Detailed Solution

Speed of fish

= 3 m/s

Speed of bird $= x m/s$

Speed of bird as seen from denser medium $= μ x$

Relative speed $= 3 + μ x$

But, relative speed $= 9 m/s$

$3 + μ x = 9$

$μ x = 6 \Rightarrow \frac{6}{μ} = \frac{6}{(4/3)} = 6 \times \frac{3}{4} = 4.5 m/s$

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A fish rising vertically to the surface of water in a lake uniformly at the rate of 3 ms−1 observes a bird diving vertically towards the water at a rate of 9 ms−1 vertically above it. If the refractive index of water is 4/3 , the actual velocity of the dive of the bird