Question

an airplane has a speed of 120km/h in still air. the plane is headed 30 degrees east of north when a wind starts blowing due east at 30km/hr. What is the planes speed relative to the ground?

Answer 1

Velocity of an airplane in still air:

$$(120 \sin{30}, 120 \cos{30}) \dfrac{km}{h}$$

Velocity of the wind is

$$(30, 0) \dfrac{km}{h}$$

Velocity of airplane relative to the ground is

$$(120 \sin{30} +30, 120 \cos{30}) \dfrac{km}{h}$$

 The plane's speed relative to the ground:

$$v=\sqrt{(120 \sin{30} +30)^2+(120 \cos{30})^2} =137.5\dfrac{km}{h}$$