Question

an airplane tries to fly due north at 100 m/s but a wind is blowing from the west at 30 m/s. what heading (angle and direction) should the plane take to go due north in spite of the wind?

Answer 1

Angle of wind from west = 45°
x-component of wind:
Wx = 30cos(45)
= 21.1 m/s

The x component of the plane's speed should cancel this while the y component should remain 100 m/s

Py = Psin(∅)
100 = Psin(∅)
P = 100/sin(∅)

Px = Pcos(∅)
P = 21.1/cos(∅)
100/sin(∅) = 21.1/cos(∅)
tan(∅) = 100/21.1
∅ = 78.1° north from the west direction.