Question

A pilot is to flag an aircraft with a velocity $v$ due east. Wind is blowing due south with a velocity $u$. Find the time for a round journey $A$ to $B$ and back. ($A$ and $B$ are $l$ distance away and $B$ is in east direction).

• A. $\frac{l}{\sqrt{v^2-u^2}}$
• B. $\frac{2l}{\sqrt{v^2-u^2}}$
• C. $\frac{2l}{v}$
• D. $\frac{2l}{\sqrt{v^2+u^2}}$

Answer 1

Answer: (B)

$\frac{2l}{\sqrt{v^2-u^2}}$

The velocity in the direction $A$ to $B$ will be $\sqrt{v^2-u^2}$
$\therefore t=\frac{l}{\sqrt{v^2-u^2}}$
same time is needed to come back from $B$ to $A$.
$\therefore t_{net}=\frac{2l}{\sqrt{v^2-u^2}}$