Question

A bird in air is at a height y from the surface of water s fish is at depth x below the surface of water the refractive index of water is mu the apperent distance of bird to the fish is

Answer 1

A fish rising vertically to the surface of water in a lake uniformly at the rate of 3 m/s observes a king fisher bird diving vertically towards water at the rate 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.

Given,
Rate at which the fist is rising = 3 m/s
Rate at which the king fisher is diving = 9 m/s 
Refractive index of water = 4/3 

If at any instant, the fish is at a depth ‘x’ below water surface while, the bird is 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 = Apparent heightReal heightμ = Apparent heightReal height

or,             Apparent height = μy 

So, the total apparent distance of the bird as seen by the fish in water will be h = x + μy 
Now, differentiating w.r.t time, we get 

                      dhdt=dxdt+μdydtdhdt=dxdt+μdydt 

⇒⇒                     9 = 3+μ(dydt)9 = 3+μdydt 

⇒⇒                 dydt = 6(4/3) = 4.5 m/s.dydt = 6(4/3) = 4.5 m/s.


Thus, the kingfisher bird is diving with a velocity of 4.5 m/s. 

Answer 2

Answer:

apparent distance from bird to fish is U X+Y