Question

A fish rising vertically to the surface of water in a lake uniformly at the rate of 3m/s observes a kingfisher diving vertically towards water at the rate of 9m/s vertically above it.Ifrefractive index of water is 4/3 .Find actual velocity of the dive of the bird​

Answer 1

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Explanation:Suppose fish is situated at a distance x from the water surface and Bird is at a distance of h from surface

so y=μh+x

Differentiating w.r.t time

dt

dy

=μ  

dt

dh

​  

+  

dt

dx

​  

 

9=μV  

bird

​  

+V  

fish

​  

 

9=  

3

4

​  

V  

bird

​  

+3

V  

Bird

​  

=(9−3)  

4

3

​  

=4.5m/s

Answer 2

Answer:

Suppose fish is situated at a distance x from the water surface and Bird is at a distance of h from surface

so y=μh+x

Differentiating w.r.t time

dtdy=μdtdh+dtdx

9=μVbird+Vfish

9=3/4Vbird+3

VBird=(9−3)4/3=4.5m/s