An airplane flies with a velocity of 55.0 m/s [35o N of W] with respect to the air (this is known as air speed). If the velocity of the airplane according to an observer on the ground is 40.0 m/s [53o N of W], what was the wind velocity?

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02-08-2022
Physics

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An airplane flies with a velocity of 55.0 m/s [35o N of W] with respect to the air (this is known as air speed). If the velocity of the airplane according to an observer on the ground is 40.0 m/s [53o N of W], what was the wind velocity?

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adioabiola adioabiola · Answer 1 · 2022-08-03T19:15:52+02:00

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.

What is the wind velocity of the according to the observed velocity?

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.