You are flying in a light airplane spotting traffic for a radio station. Your flight carries you due east above a highway. Landmarks below tell you that your speed is 46.0 m/s relative to the ground and your air speed indicator also reads 46.0m/s. However, the nose of your airplane is pointed somewhat south of east and the station's weather person tells you that the wind is blowing with speed 25.0 m/s.In which direction is the wind blowing?

Answer 1

Let i be the unit vector easy and j be the unit vector north.

Velocity relative to ground = 46 i

wind velocity = 25 cosA i + 25 sinA j
(A is measured north from east)

velocity with respect to air =
46 cosB i + 46 sinB j
(B is direction the plane is pointed, north from east)

The ground velocity vector is the sum of the two that follow.

That would require that:
25 sinA + 46 sinB = 0
25 cosA + 46 cosB = 46
Solve for angles A and B. Looks messy

Answer 2

49.7

Answer 3

122