A fish and a bird are moving as shown in the | vedclass

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(A) Let the distance of the bird from the surface be $y$ and the distance of the fish from the surface be $x$. The apparent height of the bird as seen

Vedclass · Accepted Answer

$8\, m/s$ upwards

Vedclass · Answer

(A) Let the distance of the bird from the surface be $y$ and the distance of the fish from the surface be $x$. The apparent height of the bird as seen by the fish is given by $H_{app} = \mu y + x$.Differentiating with respect to time $t$,we get the apparent velocity of the bird with respect to the fish:$v_{bf} = \frac{d}{dt}(\mu y + x) = \mu \frac{dy}{dt} + \frac{dx}{dt}$.Given:Velocity of the bird,$\frac{dy}{dt} = -12\, m/s$ (downwards,so negative).Velocity of the fish,$\frac{dx}{dt} = 24\, m/s$ (downwards,so positive relative to the fish's frame of reference for the distance $x$ increasing).Refractive index,$\mu = 4/3$.Substituting the values:$v_{bf} = \frac{4}{3}(-12) + 24$$v_{bf} = -16 + 24 = 8\, m/s$.Since the result is positive,the bird appears to be moving upwards at $8\, m/s$ as observed by the fish.

$A$ fish and a bird are moving as shown in the figure. Find the velocity of the bird as observed by the fish.

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