A fish rising vertically upward with a uniform velocity of 8 m s – 1 , observes that a bird is diving vertically downward towards the fish with the velocity of 12 m s – 1 . If the refractive index of water is 4 3 , then the actual velocity of the diving bird to pick the fish, will be __________m s - 1 .

Step-by-step solution

Let the fish be at a depth x from the surface and let the bird be at height y from the surface. So, with respect to fish y ' = μ y + x ⇒ y ' = 4 y 3 + x Differentiating with respect to time, d y ' d t = 4 d y 3 d t + d x d t ⇒ 4 y 3 + d x d t = - 12 ⇒ 4 3 · d y d t = - 12 + 8 = - 4 ⇒ d y d t = - 3   m   s - 1