Q 12-09-123JEE MainJEE Main 2023 (13 Apr, Shift 1)Medium
A fish rising vertically upward with a uniform velocity of $8\ \text{m s}^{-1}$ observes that a bird is diving vertically downward towards the fish with the velocity of $12\ \text{m s}^{-1}$. If the refractive index of water is $\dfrac43$, then the actual velocity of the diving bird to pick the fish will be ______ $\text{m s}^{-1}$.
Numerical value type. Enter your answer.
Answer: 3
To the fish, a bird at height $y$ appears at height $\mu y$. The apparent separation is $\mu y+x$, closing at
$$\mu\frac{dy}{dt}+\frac{dx}{dt}\ \Rightarrow\ \frac43v+8=12\ \Rightarrow\ v=3\ \text{m s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics