Velocity of Separation in Special Relativity

Click For Summary

Homework Help Overview

The discussion revolves around the concept of relative velocity in the context of special relativity, specifically regarding two spaceships moving apart at relativistic speeds. The original poster poses a question about determining the speed of one spaceship as viewed from the other, given their velocities relative to a stationary observer.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the relativistic velocity addition formula but expresses uncertainty about the completeness of their question due to missing information about the individual velocities of the spaceships. Some participants question the assumptions regarding the velocities of the spaceships and suggest that they are both moving at 0.99c relative to a stationary observer.

Discussion Status

The discussion includes attempts to clarify the problem and explore different interpretations of the velocities involved. While some guidance is offered regarding the need for additional information, there is no explicit consensus on the original poster's question being complete. A participant mentions finding an answer in a textbook, indicating that some productive direction has been provided.

Contextual Notes

There is a noted lack of information regarding the individual velocities of the spaceships, which is central to resolving the original question. The discussion also references a specific textbook that may contain relevant information.

AGNuke
Gold Member
Messages
455
Reaction score
9
An observer sees two spaceships flying apart with speed .99c. What is the speed of one spaceship as viewed by the other?

I considered two spaceships A and B. A is moving with velocity vA in the left direction and B is moving with velocity vB in the right direction. Hence, ##v_{sep} = v_A + v_B = 0.99c##

Now finding the relative velocity of one spaceship with respect to other.

$$v_{rel} = \frac{v_A + v_B}{1 + \frac{v_Av_B}{c^2}}$$

Now since I don't know vA or vB, I can't find the answer. So, my question here is - is my question incomplete? Or is it possible to obtain an answer.
 
Physics news on Phys.org
Your question is incomplete. you have the sum vA+vB but not the product. The product of two numbers cannot be obtained from their sum without some additional information.
 
Maybe the question means to say each ship is traveling at 0.99c relative to the stationary observer in opposite directions.
 
vela said:
Maybe the question means to say each ship is traveling at 0.99c relative to the stationary observer in opposite directions.

Hmm... I tried to look for the answer in the meantime, the book (Kleppner and Kolenkow) from which the question was lifted, fortunately provided it.

Taking your suggestion, the answer is coming out to be 0.99995c, which is the same as the answer provided.

Thanks a ton.
 

Similar threads

Is My Approach to Calculating Relative Velocity Correct?
  • · Replies 20 ·
Replies
20
Views
3K
Pulley system with relative motion
  • · Replies 2 ·
Replies
2
Views
2K
Conservation of Linear Momentum of Rigid Body
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Calculating Time Elapsed in Rocket Collision
  • · Replies 18 ·
Replies
18
Views
2K
Collision between two uniformly moving particles
  • · Replies 7 ·
Replies
7
Views
3K
Relative velocities in special relativity
  • · Replies 27 ·
Replies
27
Views
4K
How Fast Does Spaceship A Move Relative to Spaceship B?
  • · Replies 19 ·
Replies
19
Views
3K
Calculating Relative Velocity of Spaceships Using GRE Relativity Equations
  • · Replies 6 ·
Replies
6
Views
2K
(Introductory SR) Light sent from a spaceship received by Earth
  • · Replies 6 ·
Replies
6
Views
2K
Resolving Velocity Components in Constrained Motion
  • · Replies 6 ·
Replies
6
Views
4K