Question

fish rising vertically at the rate of 3 ms^–1 to the surface of water observes a kingfisher (a bird) above the water, diving vertically towards it at the rate of 9 ms^–1, the refractive index of water is 4/3. Calculate the actual velocity of the kingfisher.

• A. 4 m/s
• B. 4.5 m/s
• C. 9 m/s
• D. 12 m/s

Answer 1

Answer: (B)

4.5 m/s

Answer 2

Let actual velocity of bird = V_bird

Velocity of image when seen by fish

V_Image = µ V_bird = $\frac { 4 } { 3 }$× V_bird

The velocity of the image of the bird relative to the fish is 9 ms^–1. this is given

relative velocity of bird

w.r.t. fish = V_image – (– V_fish)

= $\frac { 4 } { 3 }$V_bird + V_fish

9 = $\frac { 4 } { 3 }$× V_bird + 3

V_bird = $\frac { 18 } { 4 }$ = 4.5 ms^–1

Option B is correct.