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in a lake ,a fish rising vertically to the surface of water uniformly at th rate of 3 m/s ,observe a bird diving vertically towards the water at a rate of 9 m/s vertically above it .calculate actual velocity of the dive of the bird.

5 years ago

Answers : (2)

Abhishek Singh
93 Points
 Velocity of bird with respect to stationary fish in water = 6m/s
 So actual vel of bird = 6/refractive index of water =4.5
5 years ago
Kushagra Madhukar
askIITians Faculty
605 Points
Dear student,
Please find the attached solution to your problem.
Speed of fish, Vf = 3 m/s
Speed of bird w.r.t fish, Vbf = – 9 m/s (Since it is in opposite direction)
Now, Vbf = Vb – Vf
Hence, Vb = Vbf + Vf = – 9 + 3 = – 6 m/s  (vertically downward direction)
If we consider the refractive index of water, n =  4/3
Let, the actual velocity of bird in air be VB
The velocity of bird for the stationary fish inside water = Vb = nVB 
Hence, VB = Vb/n = 6 x ¾ = 4.5 m/s
Hope it helps.
Thanks and regards,
4 months ago
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