# Vector Direction on XY Plane

## Homework Statement

The drawing shows two cars traveling in different directions with different speeds. Their velocities are:
vAG = velocity of car A relative to the Ground = 27.0 m/s, due east
vBG = velocity of car B relative to the Ground = 21.0 m/s, due north
The driver of car B looks out the window and sees car A. The velocity of car A relative to car B is vAB. The angle that the velocity vAB makes with respect to due east is?

## The Attempt at a Solution

I got the correct angle which is 37.9 degrees, however the answer says 37.9 degrees south of east. HOW IS IT SOUTH OF EAST?? I'm so confused, why is it not north of east? The angle is made by going 37.9 degrees NORTH of the horizontal east axis so why in the world is the answer south of east, I just do not understand.

#### Attachments

• Vector Example.gif
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Student100
Gold Member

## Homework Statement

The drawing shows two cars traveling in different directions with different speeds. Their velocities are:
vAG = velocity of car A relative to the Ground = 27.0 m/s, due east
vBG = velocity of car B relative to the Ground = 21.0 m/s, due north
The driver of car B looks out the window and sees car A. The velocity of car A relative to car B is vAB. The angle that the velocity vAB makes with respect to due east is?

## The Attempt at a Solution

I got the correct angle which is 37.9 degrees, however the answer says 37.9 degrees south of east. HOW IS IT SOUTH OF EAST?? I'm so confused, why is it not north of east? The angle is made by going 37.9 degrees NORTH of the horizontal east axis so why in the world is the answer south of east, I just do not understand.

If you were in car B, is car A receding from you? If it is receding and you're traveling north, what direction of travel would you see for car A?

If you were in car B, is car A receding from you? If it is receding and you're traveling north, what direction of travel would you see for car A?
So since car B is traveling north, it's perspective of car A is technically south?

Student100
Gold Member
So since car B is traveling north, it's perspective of car A is technically south?

Yes, think about it. If your frame of reference is car B, car A appears to be traveling south east as it's both receding from your frame, and traveling eastward.

Michele Nunes
Yes, think about it. If your frame of reference is car B, car A appears to be traveling south east as it's both receding from your frame, and traveling eastward.
Okay that makes more sense. Thank you!

Student100