Question

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

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

Answer 1

Answer: (A)

Let the actual height of bird from surface of water be $y$ and actual distance of fish from surface be $y'$ .
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
$h=x+y'h=\mu y+y'\frac{d h}{d t}=\mu \frac{d y}{d t}+\frac{d y '}{d t}\frac{d h}{d t}=\frac{4}{3}\times 9+3=15ms^{- 1}$
Hence, relative velocity of bird with respect to fish is $15ms^{- 1}$ .