First slide

Ray optics

Question

A bird is diving vertically downwards a fish in water with a velocity of 5 m/s. At the same time the fish is moving vertically downward away from the bird. If the distance of the fish as viewed by the bird remains unchanged, then velocity of the fish is $(μ = 4 / 3)$

Moderate

A

7.67 m/s
B

5.62 m/s
C

4.32 m/s
D

6.67 m/s

Solution

Distance of the fish as observed by the bird is given by
$= Z_{F / B} = x + \frac{y}{μ}$
$∴ \frac{d}{dt} (Z_{F / B}) = \frac{dx}{dt} + \frac{1}{μ} \frac{dy}{dt} = (- V_{B}) + \frac{1}{μ} V_{F}$
Since $Z_{F / B}$ is constant, we can write
$- V_{B} + \frac{1}{μ} V_{F} = O \Rightarrow V_{F} = {μV}_{B} = \frac{4}{3} \times 5 m / s = 6 .67 m / s$

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