"A plane has an airspeed of 142 m/s. A 16.0 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to Earth is due east, what is the magnitude of that velocity

vr = 142.90 m/s

the magnitude of its relative velocity is 142.90 m/s

Explanation:

Given;

A plane has an airspeed of 142 m/s (eastward)

vi = 142 m/s

16.0 m/s wind is blowing southward at the same time as the plane is flying

vb = 16.0m/s

Writing the relative velocity vector, we have;

Taking north and south as positive and negative y axis respectively, east and west as positive and negative x axis respectively.

v = 142i - 16j

The magnitude of the velocity is;

vr = √(vi^2 + vb^2)

vr = √(142^2 + 16^2)

vr = √(20420)

vr = 142.8985654231 m/s

vr = 142.90 m/s

the magnitude of its relative velocity is 142.90 m/s

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