Question

An aeroplane has to go from a point $A$ to another Point $B,500km$ away due ${30}^o$ East of north. A wind is blowing due north at a speed of $20m/s$. The air speed of the plane is $150m/s$. (a) Find the direction in which the

Answer 1

The vector diagram for various velocities is shown.Vector AC gives velocity of aeroplane relative to quiet air.Vector CB gives velocity of wind(air) relative to ground.Vector AB gives velocity of plane relative to ground.Using law of sines for triangle,

$\frac{150}{sin{30}^0}=\frac{20}{sin\theta }$.

$Therefore,sin\left(\theta \right)=\frac{20}{300}=\frac{1}{15}$. Then,

Theta=$si{n}^{-1}\frac{1}{15}={3.8}^0$.

Angle NAC=${33.8}^0$.The pilot should head the plane in the direction ${33.8}^0$ east of north