Question

A fish rising vertically up towards the surface of water with speed $3{\text{ms}}^{-1}$ observes a bird diving vertically down towards it with speed $9{\text{ms}}^{-1}$. The actual velocity of the bird is

• A. $4.5{\text{ms}}^{-1}$
• B. $5.4{\text{ms}}^{-1}$
• C. $3.0{\text{ms}}^{-1}$
• D. $3.4{\text{ms}}^{-1}$

Answer 1

The correct option is A $4.5{\text{ms}}^{-1}$


Effective height of the bird as seen by the fish,
$Y=y+\mu y^{\prime }$

Differentiating both sides w.r.t $t$

$\frac{dY}{dt}=\frac{dy}{dt}+\mu \frac{d{y}^{\prime }}{dt}$

From question,
$\frac{dY}{dt}=9{\text{ms}}^{-1};\frac{dy}{dt}=3{\text{ms}}^{-1}$

$\therefore 9=3+\frac{4}{3}\frac{d{y}^{\prime }}{dt}$

$\Rightarrow \frac{d{y}^{\prime }}{dt}=\frac{6\times 3}{4}=4.5{\text{ms}}^{-1}$

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