Question

In a lake, a fish rising vertically to the surface of water uniformly at the rate of $3m/s$, observes a bird diving vertically towards the water at a rate of $9m/s$ vertically above it. the actual velocity of the dive of the bird is : (Given refractive index water $=4/3$)

• A. $9.2m/s$
• B. $4.5m/s$
• C. $9.0m/s$
• D. $3.2m/s$

Answer 1

The correct option is B $4.5m/s$

Suppose fish is situated at a distance $x$ from the water surface and Bird is at a distance of $h$ from surface
so $y=\mu h+x$

Differentiating w.r.t time

$\frac{dy}{dt}=\mu \frac{dh}{dt}+\frac{dx}{dt}$

$9=\mu V_{bird}+V_{fish}$

$9=\frac{4}{3}{V}_{bird}+3$

$V_{Bird}=(9-3)\frac{3}{4}=4.5m/s$