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A fish rising vertically to the surface of water in a lake uniformly at the rate of $3 m/s$ observes a kingfisher (bird) diving vertically towards the water at a rate of $9 m/s$ vertically above. If the refractive index of water is $4/3$ . The actual velocity of the dive of the bird is

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15m/s

20cm/s

4.5 m/s

5.4m/s

answer is C.

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Detailed Solution

Velocity of bird w.r.t to fish

v_{B/F} = 9 m/s

Question Image

Velocity of fish w.r.t to ground $v_{F/g} = 3 m/s$

Let at some instant, situation is as shown in above diagram

The distance between bird and fish, as seen by fish

${FB}^{|} = r = x + μ y$

Differentiating w.r.t

$\frac{dr}{dt} = \frac{d x}{dt} + μ \frac{d y}{dt}$

$B_{B/F} = v_{F/g} + μ v_{B/g}$

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

$v_{B/g} = 4.5 m/s$

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