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In a lake, a fish rising vertically to t...

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 the rate of 9 m/s. The actual velocity of the dive of the bird is (given, refractive index of water = 4/3)

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If at any instant, the fish is at a depth ‘x’ below water surface while the bird at a height y above the surface, then the apparent height of the bird from the surface as seen by the fish will be given by
`m =("Apparent height")/("Real height")` or, Apparent height = py
So, the total apparent distance of the bird as seen by the fish in water will be h = x + py
or,`(dh)/(dt)= (dx)/(dt) + mu (dy)/(dt)` or `9=3+ mu((dy)/(dt))` or, `(dy)/(dt)=6/((4//3))=4.5m//s=450cm//s`
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