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Question

# A fish rising vertically to the surface of water in a lake uniformly at the rate of 2m/s observes a kingfisher diving vertically towards the water at a rate of 10m/s. If refractive index of water n=43, what will be the actual velocity of the kingfisher

A
10m/s
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B
8m/s
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C
6m/s
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D
9m/s
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Solution

## The correct option is A 6m/s∵ Velocity of bird with respect to fish, VB→F=10m/sand velocity of fish with respect to ground VF→G=2m/s∴ Distance between bird and fish, as seen by fish S=x+nyon differentiating with respect to time, we getdSdt=dxdt+ndydtVB→F=VF→G+n⋅VB→G⇒10=2+43VB→G⇒VB→G=84/3=6m/s

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