Calculate the resulting speed of an airplane with an airspeed of 120 km/h pointing due north when it encounters a wind of 90 km/h directed from the west. (recall, speed is the magnitude of velocity)

The resulting speed of the airplane is 150 Km/h

Explanation:

The airspeed of the plane is 120 Km/h due North. The wind came from West pointing to the East at 90 Km/h

Both speeds are acting in different directions, so they must be added as vectors. Both vectors and the resulting velocity (Vr) are shown in the image below

The magnitude of that velocity can be computed by using Pythagoras's theorem:

The resulting speed of the airplane is 150 Km/h