Question

^{A fish rising vertically up towards the surface of water with speed $3m{s}^{-1}$ and a bird diving vertically downwards with speed $9m{s}^{-1}$ . The velocity of bird with respect to fish is :-}

• A. $15m{s}^{-1}$
• B. $12m{s}^{-1}$
• C. $5.25m{s}^{-1}$
• D. $3.4m{s}^{-1}$

Answer 1

Answer: (A)

Let the actual height of bird from surface of water be $y$ and actual distance of fish from surface be $y^{\prime }$ .
Let the apparent height of bird as seen by fish be $x$ .
Refractive index of water,
$\mu =\frac{x}{y}x=\mu y$
Distance between fish and bird is given as
$h=x+y^{\prime }h=\mu y+y^{\prime }\frac{dh}{dt}=\mu \frac{dy}{dt}+\frac{d{y}^{\prime }}{dt}\frac{dh}{dt}=\frac{4}{3}\times 9+3=15m{s}^{-1}$
Hence, relative velocity of bird with respect to fish is $15m{s}^{-1}$ .