Question

A fish is rising up vertically inside a pond with a velocity of 4 cm/sec and notices a bird that is diving vertically downwards towards the pond and its velocity appears to be 20 cm/sec to the fish. What is the real velocity of the diving bird, if the refractive index of water is $\frac{4}{3}$?

• A. 15 cm/sec
• B. 11 cm/sec
• C. 19 cm/sec
• D. 12 cm/sec

Answer 1

The correct option is D 12 cm/sec

If at any instant the fish is at a distance x from the bottom surface while the bird is at a height h above the surface. Then the apparent height of the bird from surface as seen by fish is given by $\mu y$.
Total apparent distance as seen by the fish at a depth x below water
$h=x+\mu y$
Differentiating with respect to time
$\frac{dh}{dt}=\frac{dx}{dt}+\mu \frac{dy}{dt}$
$20=4+\frac{4}{3}\cdot \frac{dy}{dt}$
$\frac{16}{\frac{4}{3}}=\frac{dy}{dt}$
$\therefore$ actual velocity of the diving bird = $\frac{48}{4}$ = $12$ cm/sec