Why Does Car A Appear to Travel Southeast from Car B's Perspective?

In summary, the conversation discusses two cars traveling at different speeds and directions. The velocity of car A relative to the ground is 27.0 m/s to the east, while the velocity of car B relative to the ground is 21.0 m/s to the north. The angle that the velocity of car A makes with respect to due east, as seen from car B, is 37.9 degrees south of east. This is because, from car B's perspective, car A appears to be traveling in a south-easterly direction as it is both receding and traveling eastward.
  • #1
Michele Nunes
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2

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?

Homework Equations

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.
 

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  • #2
Michele Nunes said:

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?

Homework Equations

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?
 
  • #3
Student100 said:
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?
 
  • #4
Michele Nunes said:
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.
 
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  • #5
Student100 said:
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!
 
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Related to Why Does Car A Appear to Travel Southeast from Car B's Perspective?

1. What is a vector direction on the XY plane?

A vector direction on the XY plane refers to the direction in which a vector is pointing on a two-dimensional coordinate system. This can be described using a combination of a magnitude (length) and an angle with respect to a reference axis.

2. How is vector direction represented on the XY plane?

Vector direction on the XY plane is typically represented using an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude of the vector. The angle between the vector and a reference axis (usually the x-axis) is also shown.

3. Can a vector have a negative direction on the XY plane?

Yes, a vector can have a negative direction on the XY plane. This means that the vector is pointing in the opposite direction of the reference axis, and the angle will be measured in the opposite direction as well.

4. How is the direction of a vector on the XY plane determined?

The direction of a vector on the XY plane is determined by the angle it makes with a reference axis (usually the x-axis). This angle can be measured using trigonometric functions such as sine, cosine, and tangent.

5. What is the difference between a vector's direction and its magnitude on the XY plane?

The direction of a vector on the XY plane refers to the angle at which the vector is pointing, while the magnitude refers to the length of the vector. Both the direction and magnitude are needed to fully describe a vector on the XY plane.

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