A fish rising vertically to the surface of water in a lake uniformly at the rate of 2 m / s observes a kingfisher diving vertically towards the water at a rate of 10 m / s . If refractive index of wat

Question

A fish rising vertically to the surface of water in a lake uniformly at the rate of 2 m / s observes a kingfisher diving vertically towards the water at a rate of 10 m / s . If refractive index of water n = 3 4 ​ , what will be the actual velocity of the kingfisher

TestHub · Accepted Answer

∵ Velocity of bird w.r.t. fish, v B → F ​ = 10 m / s and velocity of fish w.r.t. ground V F → G ​ = 2 m / s ∴ Distance between bird and fish, as seen by fish S = x + n y on differentiating w.r.t. time, we get ​ d t d S ​ = d t d x ​ + n d t d y ​ v B → F ​ = v F → G ​ + n ⋅ v B → G ​ ⇒ 10 = 2 + 3 4 ​ v B → G ​ ⇒ v B → G ​ = 4/3 8 ​ = 6 m / s ​

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