Question

A fish rising vertically to the surface of water in a lake uniformly at the rate of $2m/s$ observes a kingfisher diving vertically towards the water at a rate of $10m/s$. If refractive index of water $n=\frac{4}{3}$, what will be the actual velocity of the kingfisher

• A. $10m/s$
• B. $8m/s$
• C. $6m/s$
• D. $9m/s$

Answer 1

Answer: (C)

$6m/s$

$\because$ Velocity of bird with respect to fish,
$V_{B\to F}=10m/s$
and velocity of fish with respect to ground
$V_{F\to G}=2m/s$
$\therefore$ Distance between bird and fish, as seen by fish
$S=x+ny$
on differentiating with respect to time, we get
$\frac{dS}{dt}=\frac{dx}{dt}+n\frac{dy}{dt}$
$V_{B\to F}=V_{F\to G}+n\cdot V_{B\to G}$
$\Rightarrow 10=2+\frac{4}{3}{V}_{B\to G}$
$\Rightarrow V_{B\to G}=\frac{8}{4/3}=6m/s$