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Question

In a lake, a fish rising vertically to the surface of water uniformly at the rate of 3 m/s, observes a bird diving vertically towards the water at a rate of 9 m/s vertically above it. the actual velocity of the dive of the bird is : (Given refractive index water =4/3)

A
9.2 m/s
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B
4.5 m/s
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C
9.0 m/s
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D
3.2 m/s
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Solution

The correct option is B 4.5 m/sSuppose fish is situated at a distance x from the water surface and Bird is at a distance of h from surfaceso y=μh+xDifferentiating w.r.t timedydt=μdhdt+dxdt9=μVbird+Vfish9=43Vbird+3VBird=(9−3)34=4.5m/s

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