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)130 m/s
B)16 m/s
C)160 m/s
D)141 m/s
E)48 m/s

Question

Quizplus · Accepted Answer

We need to use vector addition since we have two velocities at different directions. Let eastward direction be positive and northward direction be negative.

Let's call the velocity of the plane relative to the ground as V and the velocity of the wind as W. We know that V has a component going eastward and a component going southward. We also know that W is going southward.

Using Pythagorean theorem, we can find the magnitude of V:

V² = (142 m/s)² + (16 m/s)² 
V² = 20160 
V = √20160 
V ≈ 141 m/s

Therefore, the magnitude of the velocity of the plane relative to the ground is 141 m/s.

A Plane Has an Airspeed of 142 M/s