Question

An aeroplane has to go from a point $A$ to $B$ due north. Wind is blowing due east at a speed of $250\text{km/h}$. If the air speed of plane is $500\text{km/h}$ then its direction of head to reach point $B$ is

• A. ${15}^{\circ }$ west of north
• B. ${60}^{\circ }$ west of north
• C. ${45}^{\circ }$ west of north
• D. ${30}^{\circ }$ west of north

Answer 1

The correct option is D ${30}^{\circ }$ west of north

Let us suppose aeroplane heads at an angle of $\theta$ west of north.
The data given in the question is shown in the figure below.

To reach from point $A$ to $B$, velocity $\left(v_n\right)$ of aeroplane should be along the direction of $AB$.
$\therefore$ velocity along x-axis should be equal to zero.
$\Rightarrow \sum v_x=0$
$\Rightarrow 250-500\sin \theta =0$
$\sin \theta =\frac{1}{2}$
$\Rightarrow \theta ={30}^{\circ }$
The aeroplane should head at an angle of ${30}^{\circ }$ west of north.
Hence, option(d) is correct answer.