Relative velocity of 2 particles

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SUMMARY

The discussion centers on calculating the relative velocity of two particles emitted from opposite ends of a linear particle accelerator, with speeds of 0.5c and 0.6c, respectively. The correct approach involves using the relativistic velocity addition formula, which is essential for accurately determining the relative speed between two objects moving at significant fractions of the speed of light. The formula VPE = (VPA + VAE) / (1 + (VPA * VAE / c²) ) should be applied to find the relative velocity. The participants emphasize the need for a deeper understanding of relativistic velocity concepts, as traditional methods do not suffice.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with the relativistic velocity addition formula
  • Basic knowledge of particle physics
  • Ability to perform calculations involving fractions of the speed of light
NEXT STEPS
  • Study the relativistic velocity addition formula in detail
  • Explore examples of relative velocity in particle physics
  • Review the implications of special relativity on high-speed particle interactions
  • Investigate resources on hyperphysics for further clarification on relativistic concepts
USEFUL FOR

Students and educators in physics, particularly those focusing on special relativity and particle dynamics, as well as anyone involved in high-energy physics research.

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Homework Statement



Two particles are emitted from opposite ends of a linear particle accelerator, one with a speed of 0.5 c and the other with a speed of 0.6 c, relative to the accelerator.

What is the relative speed of the two particles?


Homework Equations



VPE = VPA + VAE

The Attempt at a Solution


I understand that there is relative velocity between:
A particle to the accelerator (V [subscript] PA )
A particle to the other particle ( V [subscript] PP)

How would I continue?
We haven't gone in depth for Rel. vel. between two moving objects - only between an object and the ground, but that section was very brief.
 
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