How Do You Calculate Relative Speed in Special Relativity?

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Homework Help Overview

The problem involves calculating the relative speed of two spaceships moving in opposite directions, as measured by an observer on Earth. The speeds of the spaceships are given as fractions of the speed of light (c), and the context is rooted in the principles of special relativity.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply Galilean relativity initially but realizes the need for Einstein's velocity addition formula due to the relativistic speeds involved. Some participants provide references to the relevant formula and share their calculations, questioning the correctness of their results.

Discussion Status

The discussion includes attempts to verify the calculations related to the relative speed of the spaceships. Some participants express uncertainty about their results and seek confirmation, while others affirm the correctness of the calculations based on the conventions used.

Contextual Notes

Participants are navigating the complexities of special relativity and the implications of using different conventions for speed, particularly regarding the signs of the velocities involved.

Jalo
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Homework Statement



Two spaceships (A and B) are traveling in opposite ways. An observer in Earth measures both velocities.
The speed of ship A (Va) = 0.75c.
The speed of ship B (Vb) = 0.85c.
What's the speed of **** B regarding ship A?

Homework Equations


The Attempt at a Solution



At first I tried solving it using Galileu's relativity, but I've reached the result of 1.6c.
Then I remembered that when we're dealing with speeds close to c we have to use Einstein's special relativity, so I've looked around all the formulas I have but none of them involved velocity, only time, spaceship length, and there are also the ones involving energy but I don't think that has nothing to do with this exercise.

Thanks!
 
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Doc Al said:
Read: Einstein Velocity Addition

I've used u'= -.85c and v=.75c

Substituting I got u= -.85c-.75c / 1-(-.85*.75) = -.977c

Therefore the speed of ship B regarding ship A is -0.977c

Is that solution correct? I think I've done everything right but i'd like to be sure :D

Thanks!
 
Good. The relative speed is correct, which is all you need. (The sign depends on your convention.)
 

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