A fish rising vertically upward with a uniform velocity of 8 ms⁻¹, observes that a bird is diving vertically downward towards the fish with the velocity of 12 ms⁻¹. If the refractive index of water is 4/3, then the actual velocity of the diving bird to pick the fish, will be __________ ms⁻¹. Numerical answer type. Work it out, then open the answer.

Answer: 3. Fish in water at depth x, bird at height y in air. Fish sees the bird at apparent height μ y above the surface. Apparent separation seen by fish: D = x + μ y, so |dD/dt| = vf + μ vb. 12 = 8 + 4/3vb vb = 4 × 3/4 = 3 So the actual speed of the bird is 3 ms⁻¹.

A fish rising vertically upward with a uniform velocity of 8 ms⁻¹… | JEE Main 2023 (13 Apr, Shift 1)

Q40JEE Main 2023 · 13 APR · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

A fish rising vertically upward with a uniform velocity of $8\text{ ms}^{-1}$ , observes that a bird is diving vertically downward towards the fish with the velocity of $12\text{ ms}^{-1}$ . If the refractive index of water is $\frac{4}{3}$ , then the actual velocity of the diving bird to pick the fish, will be __________ $\text{ms}^{-1}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 3

Fish in water at depth $x$ , bird at height $y$ in air. Fish sees the bird at apparent height $\mu y$ above the surface.
Apparent separation seen by fish: $D = x + \mu y$ , so $\left|\frac{dD}{dt}\right| = v_f + \mu v_b$ .
$12 = 8 + \frac{4}{3}v_b$
$v_b = 4 \times \frac{3}{4} = 3$
So the actual speed of the bird is $3\text{ ms}^{-1}$ .

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