Question

An aeroplane flies along a straight line from A to B with air speed $V$ and back again with the same air speed.If the distance between A and B is $l$ and a steady wind blows perpendicular to AB with speed $u$, the total time taken for the round trip is

• A. $\frac{2l}{\sqrt{V^2-u^2}}$
• B. $\frac{2l}{\sqrt{V^2+u^2}}$
• C. $\frac{l}{\sqrt{V^2-u^2}}$
• D. $\frac{3l}{\sqrt{V^2-u^2}}$

Answer 1

The correct option is A $\frac{2l}{\sqrt{V^2-u^2}}$

If the plane has to fly in straight line then he must fly at some angle theta with the AB. And component of velocity of plane in direction of air flow with respect to ground should be zero. i.e. $u=vSin\theta$. From here $Sin\theta =\frac{u}{v}$

And component of velocity of plane which will help plane to cover the distance $l$ is $vCos\theta$

So time taken to cover distance $l$ is given by $\frac{l}{vCos\theta }$ and $Cos\theta =\sqrt{1-(\frac{u}{v}{)}^2}$.

So time taken from A to B is $\frac{l}{\sqrt{v^2-u^2}}$ same will be case while returning so total time will be $\frac{2l}{\sqrt{v^2-u^2}}$

So best option is A.