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: $Vsin\theta =v$
$sin\theta =\frac{v}{V}$
$\therefore t=t_{AB}+t_{BA}$
$t=\frac{2\ell }{Vcos\theta }=\frac{2\ell }{V\sqrt{1-\frac{v^2}{V^2}}}$
$\Rightarrow t=\frac{2\ell }{\sqrt{V^2-v^2}}$