Question

A ball is dropped from a height of $20\text{m}$ above the surface of water in a lake. The refractive index of water is $\frac{4}{3}$. A fish inside the lake in the line of fall of the ball is looking at the ball. At an instant when the ball is $12.8\text{m}$ above the water surface, the fish sees the speed of the ball as

• A. $9{\text{ms}}^{-1}$
• B. $21.33{\text{ms}}^{-1}$
• C. $12{\text{ms}}^{-1}$
• D. $16{\text{ms}}^{-1}$

Answer 1

The correct option is D $16{\text{ms}}^{-1}$

For free fall, velocity of ball is

$v_{ball}^2=2gh=2\times \left(10\right)\left(7.2\right)$

$\Rightarrow v_{ball}=12{\text{ms}}^{-1}$

To the fish, the image of the ball will appear as elevated, so

$X_{\text{image of ball}}={\mu }_w\times X_{\text{ball}}$

Differentiating, $V_{\text{image}}=\frac{4}{3}\left(V_{\text{ball}}\right)=\frac{4}{3}\left(12{\text{ms}}^{-1}\right)=16{\text{ms}}^{-1}$