The wind velocity of the plane in discuss can be evaluated by means of the air velocity if the plane and the observed velocity is; 20.98m/s.
It follows from the task content that the air velocity of the plane in discuss is; 55.0 m/s [35o N of W] while the observed velocity is; 40.0 m/s [53o N of W].
Hence, the components of both velocities can be evaluated as follows;
55.0 m/s [35o N of W] = (55cos35, 55sin35) = (45.05, 31.55)
40.0 m/s [53o N of W] = (24.07, 31.95)
Hence, the wind velocity can then be evaluated as follows;
Wind velocity = (24.07 - 45.05, 31.95- 31.55)
Wind velocity = (-20.98, 0.40)
The wind velocity would therefore have a magnitude of; √(-20.98)² + (0.40)²
= 20.98 m/s.
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