An aeroplane has to go from a point A to another point B, 500 km away due ${30}^0$ east of north. A wind is blowing due north at as speed of 20 m/s. The air-speed of the plane is 150 m/s.

(a) Find the directiion in which the pilot should head the plane to reach the point B.

(b) Find the time taken by the plane to go from A to B.

In resultant direction $\overrightarrow{R}$, the plane reaches the point B.

Velocity if wind, ${\overrightarrow{V}}_m$= 20 m/s

Velocity of aeroplane, $V_a$ = 150 m/s

In $\Delta$ACD, according to since formula

$\therefore \frac{20}{sinA}=\frac{150}{sin{30}^0}$

$\Rightarrow sinA=\frac{20}{150}sin{30}^0$

=$\frac{20}{150}\times \frac{1}{2}\times =\frac{1}{15}$

$\Rightarrow A=si{n}^{-1}\left(\frac{1}{15}\right)$

(a) The direction is $si{n}^{-1}\left(\frac{1}{15}\right)$ east of the line AB.

$si{n}^{-}1\frac{1}{15}=3^0{18}^{\prime }$

$\Rightarrow {30}^0+3^{+}{48}^{\prime }={33}^4{8}^0$

R = $\sqrt{150+20+2\left(150\right)20cos\left({33}^0{48}^{\prime }\right)}$

= $\sqrt{2}7886=167km/s$

(b) time = $\frac{s}{v}=\frac{500000}{167}$

= $2994sec$ = 49.0$\approx$ 50 min