Relative Velocities A & B: 5MPH Each

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In summary, the topic of relative velocity and its calculation using the velocity-addition formula was discussed. It was mentioned that the formula becomes more significant at higher speeds, particularly when approaching light speeds. An example was given where A and B approached each other at 5 MPH with respect to a third frame, resulting in a relative velocity of nearly 10 MPH. It was also noted that the approximation formula for adding velocities is accurate for low speeds, but becomes less so at higher speeds. Overall, the conversation provided a deeper understanding of the complexities of relative velocity and its calculations.
  • #1
ssope
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A approaches B at 5 MPH
B approaches A at 5 MPH

I am wondering why at very fast speeds, the error would become quite large if you were to say that A and B's relative velocity is equal to 10.
 
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  • #2
ssope said:
A approaches B at 5 MPH
B approaches A at 5 MPH
I assume you mean something like this:
A moves towards B at a speed of 5 mph with respect to some frame C.
B moves towards A at a speed of 5 mph with respect to some frame C.

I am wondering why at very fast speeds, the error would become quite large if you were to say that A and B's relative velocity is equal to 10.
It's a conclusion of special relativity that velocities do not add simply as V1 + V2. Read all about it: http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html"

(Edit: I forgot to add the punchline, that the difference becomes marked when speeds approach light speeds. DaleSpam got it.)
 
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  • #3
Hi ssope, welcome to PF.

The correct formula for adding velocities is called the http://en.wikipedia.org/wiki/Velocity-addition_formula" :

[tex]\frac{v_1+v_2}{\frac{v_1 v_2}{c^2}+1}[/tex]

In your case
[tex]\frac{5+5}{\frac{5 \times 5}{(6.7 \times 10^8)^2}+1} = 9.9999999999999994 \, mph[/tex]

For such low velocities the difference between the real formula and the approximation is undetectable, less than 1 micrometer/century.
 
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  • #4
Hi,
A approaches C at 5 MPH
C approaches B at 5 MPH
Then
For C: A and B's relative velocity of approach equal to 10.
For A: the velocity of B is less than 10.
For B: the velocity of A is less than 10.
Regards.
 
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  • #5
Thank you all very much for answering my question.
 

Related to Relative Velocities A & B: 5MPH Each

1. What are relative velocities A & B?

Relative velocities A & B refer to the speeds of two objects in relation to each other. In this case, both objects are moving at a constant speed of 5 miles per hour.

2. How do you calculate relative velocity?

To calculate relative velocity, you subtract the velocity of one object from the velocity of the other object. In this case, the relative velocity of A with respect to B would be 5 miles per hour, and the relative velocity of B with respect to A would also be 5 miles per hour.

3. What is the difference between relative velocity and absolute velocity?

Relative velocity takes into account the motion of two objects in relation to each other, while absolute velocity refers to the motion of an object in relation to a fixed point or frame of reference. In this case, the absolute velocity of both objects would also be 5 miles per hour.

4. Can relative velocity be negative?

Yes, relative velocity can be negative if one object is moving in the opposite direction of the other object. In this case, if object A was moving at 5 miles per hour in the positive direction and object B was moving at 5 miles per hour in the negative direction, the relative velocity of A with respect to B would be 10 miles per hour in the negative direction.

5. How does relative velocity affect collisions between objects?

Relative velocity plays a crucial role in collisions between objects. The relative velocity of two objects at the point of collision determines the impact and resulting damage. In this case, if both objects are moving at 5 miles per hour, the resulting collision would have an impact of 10 miles per hour.

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