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In a lake, a fish rising vertically to the surface of water uniformly at the rate of \mathrm{3\ m/s}, observes a bird diving vertically towards the water at the rate of \mathrm{9\ m/s}. The actual velocity of the dive of the bird is (given, refractive index of water \mathrm{=4/3})

Option: 1

\mathrm{3.6\ m/s}


Option: 2

\mathrm{4.5\ m/s}


Option: 3

\mathrm{6.0\ m/s}


Option: 4

\mathrm{12.0\ m/s}


Answers (1)

best_answer

Fish is observer and bird is object.

Apparent distance between \mathrm{F} and \mathrm{B} at some instant will be,
\mathrm{y=\left ( x+\mu h \right )}
\mathrm{\begin{aligned} & \left(-\frac{\mathrm{dy}}{\mathrm{dt}}\right)=\left(-\frac{\mathrm{dx}}{\mathrm{dt}}\right)+(\mu)\left(-\frac{\mathrm{dh}}{\mathrm{dt}}\right) \\ & 9=3+\frac{4}{3}\left(-\frac{\mathrm{dh}}{\mathrm{dt}}\right) \\ & \therefore \quad-\frac{\mathrm{dh}}{\mathrm{dt}}=4.5 \mathrm{~m} / \mathrm{s} \end{aligned}}

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Ritika Kankaria

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