Question
Wed November 21, 2012 By:

A fish is raising vertially to the surface of water in a lake uniformly at the rate of 2m/s observes a bird diving vertically towards water at a rate of 4m/s vertically above it.the refractive index of water is 4/3.what is the actual velocity of the bird?

Expert Reply
Thu November 22, 2012
Ans. 1.5m/s
If at any instant the fish is at the depth 'x' below fish 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
µ =  or Apparent height = µy
So, the total apparent distance of the bird as seen by the fish in water will be
h = x + µy
or 
         4= 2 + µ()
dy/dt =2/(4/3)=6/4=3/2=1.5m/s
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