Question

A fish is rising up vertically inside a pond with velocity $4\text{cm/s}$ and notices a bird, which is diving downward and its velocity appears to be $16\text{cm/s}$ (to the fish). The real velocity of the diving bird is $[{\mu }_{\text{water}}=4/3]$

• A. $9\text{cm/s}$
• B. $12\text{cm/s}$
• C. $6\text{cm/s}$
• D. $15\text{cm/s}$

Answer 1

The correct option is A $9\text{cm/s}$


Given, $\frac{-dy}{dt}=4\text{cm/s}$

By apparent height formula, distance of bird as observed by fish,
$z=y+\mu x$
&$\frac{-dz}{dt}=16\text{cm/s}$

Differentiating both sides, we get

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

As the distances are decreasing, thus,

$\frac{-dz}{dt}=\frac{-dy}{dt}-\frac{\mu dx}{dt}$

$\Rightarrow 16=4-\frac{4}{3}\frac{dx}{dt}$

$\Rightarrow \frac{-dx}{dt}=\frac{12\times 3}{4}=9\text{cm/s}$

So, real velocity of the diving bird is $9\text{cm/s}$.

Why this question ? This question tests your skill on instantaneous speed and apparent speed. Such questions are very important from JEE point of view