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

Distance of bird as observed by fish,

$z=y+\mu x=y+\frac{4}{3}x[\because \mu =\frac{h_{\text{app}}}{h_{\text{real}}}]$

differentiating both side w.r.t $t$, we get

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

As the distances are decreasing, thus

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

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

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

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

Therefore, $\left(a\right)$ is the correct option.

$\begin{array}{c}\text{Why this question ?}\\ \text{This question test the skill of instantaneous}\\ \text{speed and apparent speed.}\end{array}$