Question

A plane is flying at 300km/h [S 39 E]. The wind is blowing at 60 km/h [N 75 E]. What is the velocity of the plane relative to the ground?

Answer 1

Angle between the plane and wind is

$$180-75-39=66\degree$$

Now relative velocity of plane wrt. ground is

$$v_{pg}=v_{pw}+v_{wg}=\sqrt{300^2+60^2+2\times 300\times 60\cos66\degree}$$

$$329\ km\ h^{-1}$$

For direcrion-

$$\theta=tan^{-1}(\frac{60sin66\degree}{300+60cos66\degree})=9.584\degree$$

So the direction is $9.584\degree$ anticlockwise from the direction of plane .