First slide

Refraction of light

Question

A fish rising up vertically toward the surface of water with speed 3 ms^-1 observes a bird diving down vertically towards it with speed 9 ms^-1. The actual velocity of bird is

Moderate

A

4.5 m s^-1
B

5.4 m s^-1
C

3.0 m s^-1
D

3.4 m s^-1

Solution

Effective height of the bird as seen by the fish, Y = y + $μ$ y'
$\frac{dY}{dt} = \frac{dy}{dt} + μ \frac{dy'}{dt} 9 = + 3 + \frac{4}{3} \frac{dy'}{dt} or \frac{dy'}{dt} = \frac{6 \times 3}{4} = \frac{18}{4} = \frac{9}{2} = 4.5 m s^{- 1}$
Therefore, actual velocity of bird = 4.5 m s^-1

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