Question

An airplane flies with a velocity of 45.0 m/s [ W 35^o N] with respect to the air (this is known as air speed). If the velocity of the airplane according to a stationary observer on the ground is 30.0 m/s [W 60^o N], what was the wind velocity?

Answer 1

The magnitude of the wind velocity can be found using the law of cosines.

c^2 = a^2 + b^2 - 2*a*b*cos(C)

C = angle between the two vectors = 65 - 35 = 30 degrees
c^2 = 45^2 + 30^2 - 2*45*30*cos(30) = 586.73
c = 24.22 m/s

wind speed = 24.22 m/s