Question

An airplane pilot wish to fly due west while wind is blowing towards south at $100\text{km/hr}$ . If the speed of the airplane with respect to blowing wind is $200\text{km/hr}$, in which direction should the pilot head to reach the destination ?

• A. ${60}^{\circ }$ South of West
• B. ${30}^{\circ }$ West of North
• C. ${30}^{\circ }$ North of West
• D. ${45}^{\circ }$ North of West

Answer 1

The correct option is C ${30}^{\circ }$ North of West


Velocity of wind w.r.t ground:
${\overrightarrow{v}}_{WG}=100\text{km/hr}$

Velocity of plane w.r.t wind:
${\overrightarrow{v}}_{PW}=200\text{km/hr}$

${\overrightarrow{v}}_{PG}$ is velocity of plane w.r.t ground

$\therefore {\overrightarrow{v}}_{PG}={\overrightarrow{v}}_{PW}+{\overrightarrow{v}}_{WG}$

$\Rightarrow$ From vector triangle shown in figure, if plane has to move towards west direction, then it has to fly at angle $\theta$ with west so, that resultant velocity $v_{PG}$ is in west direction.

Thus, from vector triangle:

$\therefore v_{PW}\sin \theta =v_{WG}$

$\sin \theta =\frac{{\overrightarrow{v}}_{WG}}{{\overrightarrow{v}}_{PW}}=\frac{100}{200}=\frac{1}{2}$

$\therefore \theta ={30}^{\circ }$ North of West, required heading direction for pilot.