Question

A fish is moving up vertically with speed 4 cm/s inside a pond. A bird is moving vertically downward (see figure). Velocity of the bird w.r.t. fish is 16 cm/s downward. Find out the actual velocity of the bird (in cm/s). Given refractive index of water is $\frac{4}{3}$.

Answer 1

${\overrightarrow{v}}_{BF}={\overrightarrow{v}}_{BG}-{\overrightarrow{F}}_{FG}$
$\Rightarrow \frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=0$

$\Rightarrow \frac{\frac{4}{3}}{v}-\frac{i}{u}=0$

$\Rightarrow \frac{4}{3v}=\frac{1}{u}\Rightarrow v=\frac{4u}{3}\Rightarrow v=\frac{4u}{3}\Rightarrow \frac{dv}{dt}=\frac{4}{3}\frac{du}{dt}$

$16=\frac{4u}{3}+4\Rightarrow 12=\frac{4u}{3}\Rightarrow u=9cm/s$