Special Relativity Velocity Transformation

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Homework Help Overview

The discussion revolves around a problem in special relativity concerning the velocity transformation of two particles moving in perpendicular directions at the same speed in an inertial frame. The original poster expresses difficulty in approaching the problem, particularly because previous experiences with velocity transformations involved particles moving in parallel or opposite directions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the concept of relative velocity between two particles moving orthogonally, with one suggesting the use of multiple frames of reference to analyze the situation. The original poster questions how to apply previous knowledge to this new context.

Discussion Status

The discussion has seen contributions that suggest different approaches, including the use of various frames of reference. The original poster indicates progress after exploring multiple methods, although no specific consensus or resolution is stated.

Contextual Notes

The original poster mentions a struggle with the problem setup, indicating a potential gap in understanding how to apply velocity transformations in this specific scenario. There is an implication of homework constraints, as the original poster seeks help without revealing a complete solution.

mike_romeo
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Hi,
I'm struggling with a special relativity question

Two particles are traveling in an inertial frame in perpendicular directions to each other at velocity v. Calculate the velocity of each particle relative to the other


I'm not sure how to approach it. In the past any velocity transformations I have done have always been for particles traveling in the same or opposite directions, not orthogonally?


Any help appreciated!
 
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If one of the particles (particle I) was intelligent and was able to 'see' the other one, it would see that the other particle was coming in at an angle, which is due to particle I moving toward the other particle and also due to how the other particle is moving in the given direction.
 
Hi mike romeo, welcome to PF!:smile:

Try treating the problem using 3 frames of reference; the lab frame [itex]S[/itex], particle 1's rest frame [itex]S'[/itex] and particle 2's rest frame [itex]S''[/itex]...set up your coordinate axes however you want and then calculate away...
 
Thanks for the replies, sorry for taking a while to get back to you both.

I got it in the end after countless pages of working out trying different methods and the ones you mentioned.

Thanks again
 

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