A fish rising vertically to the surface of water in a lake 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. If the refractive index of water is (4/3), find the actual velocity of the dive of the bird.

Explanation

If at any instant, the fish is at a depth x below the water surface while the bird is at a height y above the surface, then the apparent height of the bird above the surface as seen - by fish will be `y_(ap) = mu_y`
So the total apparent distance of the bird as seen by fish in water at depth x will be `h= x + mu y `(or)
`(dh)/( dt) =(dx)/(dt) + mu ( dy )/(dt),i.e., 9= 3 + mu (dy )/( dt)`
`i.e., (dy)/(dt) = (6)/( (4//3)) = 4.5 m//s`