Question

An aeroplane is to go along straight line from $A$ to $B$, and back again. The relative speed with respect to wind is $V$. The wind blows perpendicular to line $AB$ with speed $v$ The distance between $A$ and $B$ is $l$ The total time for the round trip is

• A. $\frac{2 \ell}{\sqrt{V^{2}-v^{2}}}$
• B. $\frac{2V \ell}{V^{2}-v^{2}}$
• C. $\frac{2V\,\ell}{V^{2}-v^{2}}$
• D. $\frac{2 \ell}{\sqrt{V^{2}+v^{2}}}$

Answer 1

Answer: (A)

For no drift: $V\,sin\, \theta= v$
$sin\,\theta=\frac{v}{V}$
$\therefore t=t_{AB}+t_{BA}$
$t=\frac{2\ell}{V\,cos\,\theta}=\frac{2\ell}{V \sqrt{1-\frac{v^{2}}{V^{2}}}}$
$\Rightarrow t=\frac{2\ell}{\sqrt{V^{2}-v^{2}}}$