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?
A) 16.2 m/s
B) 16.0 m/s
C) 158 m/s
D) 141 m/s
E) 48 m/s

Question

Quizplus · Accepted Answer

We need to find the magnitude of the velocity vector of the plane relative to Earth.

Let the velocity of the plane with respect to Earth be v, and let the wind velocity be w. Since the plane is flying due east, its velocity relative to the air is also due east.

Therefore, the velocity vector of the plane relative to Earth can be represented as the vector sum of the velocity vector of the plane relative to the air and the velocity vector of the wind:

v = (142 m/s) + (-16.0 m/s)

The negative sign in front of the wind velocity indicates that the wind is blowing in the opposite direction to the direction the plane is flying.

Taking the magnitudes of both sides, we get:

|v| = |(142 m/s) + (-16.0 m/s)|

|v| = |126 m/s|

So the magnitude of the velocity vector of the plane relative to Earth is 126 m/s, which is closest to answer choice D: 141 m/s.

A Plane Has an Airspeed of 142 M/s