Question

An aeroplane flies from $P$ and $Q$ with speed $v$ and then from $Q$ and $P$ with the same speed. If wind blows normal to straight line $PQ$ with the speed $V$, the total time for to and fro motion is

• A. $\frac{L}{(v^2-V^2{)}^{\frac{1}{2}}}$
• B. $\frac{2L}{(v^2-V^2{)}^{\frac{1}{2}}}$
• C. $\frac{2L}{V-v}$
• D. $\frac{2L}{(v^2-V^2)}$

Answer 1

The correct option is A $\frac{L}{(v^2-V^2{)}^{\frac{1}{2}}}$

The aeroplane has to follow a path such that resultant of $v$ and $V$ should be in line with $PQ$
Thus $R=\sqrt{v^2-V^2}$ time taken to cover distance $PQ=\frac{L}{\sqrt{v^2-V^2}}$
Since velocity is same during return also/time taken to cover distance,
$QP=\frac{L}{\sqrt{v^2-V^2}}$
Thus, total time $=\frac{L}{\sqrt{v^2-V^2}}$