A plane has an airspeed of 142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity?
A) 48 m/s
B) 130 m/s
C) 16 m/s
D) 141 m/s
E) 160 m/s

Question

A plane has an airspeed of  142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity?
A)  48 m/s
B)  130 m/s
C)  16 m/s
D)  141 m/s
E)  160 m/s

Quizplus · Accepted Answer

The magnitude of the velocity of the plane relative to the ground is found by subtracting the wind's velocity vector from the plane's airspeed vector. Since the wind is blowing southward and the plane's ground velocity is directly eastward, the wind's effect is perpendicular to the plane's direction of travel. Using the Pythagorean theorem, $ \sqrt{142^2 - 16^2} = 141 $ m/s, which is the plane's velocity relative to the ground.

A Plane Has an Airspeed of 142 M/s