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?

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.