In a pond, a fish at rest sees a bird diving vertically towards water at the rate of $3$ m/s vertically above the fish. If the refractive index of water is $\frac{4}{3}$ what is the actual speed of the bird.

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Answer 1

Given data
Fish at rest
$V_{B F} = 3 m / s$ downward (Speed of Bird seen by fish)
$μ = 4 / 3$
actual speed of Bird =?
We know that,
$\frac{d y}{d t} = 0 \to$ speed of fish
Distance of Bird from fish
$R d = y + x_{a p p}$
$R = y + μ x$
Differentiating w.r.t time
$\frac{d R}{d t} = \frac{d y}{d t} + μ \frac{d x}{d t}$ (given $\frac{d R}{d t} = 3 m / s$ )
$3 = 0 + \frac{4}{3} \times \frac{d x}{d t}$

$\frac{d x}{d t} = \frac{9}{4} = 2.25 m / s \to$ Actual speed of Bird

Answer 2

Given data

Fish at rest

V_{B F} = 3 m / s

downward (Speed of Bird seen by fish)

μ = 4 / 3

actual speed of Bird =?

We know that,

\frac{d y}{d t} = 0 \to

speed of fish

Distance of Bird from fish

R d = y + x_{a p p}

R = y + μ x

Differentiating w.r.t time

\frac{d R}{d t} = \frac{d y}{d t} + μ \frac{d x}{d t}

(given

\frac{d R}{d t} = 3 m / s

)

3 = 0 + \frac{4}{3} \times \frac{d x}{d t}

\frac{d x}{d t} = \frac{9}{4} = 2.25 m / s \to

Actual speed of Bird