When and Where Will Spaceships #1 and #2 Meet in Special Relativity?

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SUMMARY

The discussion focuses on calculating the meeting point of two spaceships in the context of special relativity. Spaceship #1 travels at 0.2c, while Spaceship #2 moves at 0.6c, starting 3 x 10^9 meters behind. The relative velocity of Spaceship #2 in the inertial reference frame (IRF) of Spaceship #1 is calculated to be 0.7143c. The recommended approach is to first determine the meeting time and location in reference frame S using classical mechanics, followed by applying the Lorentz transformation to find the corresponding time in the frame of Spaceship #1.

PREREQUISITES
  • Understanding of special relativity concepts, including relative velocity.
  • Familiarity with Lorentz transformations.
  • Basic knowledge of classical mechanics for calculating motion.
  • Ability to work with velocities expressed as fractions of the speed of light (c).
NEXT STEPS
  • Calculate the meeting time and position of the spaceships in reference frame S using classical equations of motion.
  • Apply Lorentz transformations to convert the meeting time and position to the frame of Spaceship #1.
  • Explore the implications of relative velocity in special relativity for objects moving at significant fractions of c.
  • Study the effects of time dilation and length contraction on the perception of events in different reference frames.
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Students of physics, particularly those studying special relativity, as well as educators and anyone interested in the practical applications of relativistic concepts in motion and velocity calculations.

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Spaceships--special relativity

Homework Statement


Spaceship #1 moves with a velocity of .2c in the positive x direction of reference frame S. Spaceship #2, moving in the same direction with a speed of .6c is 3 x 10^9 m behind. At what times in reference frames S, and in the reference frame of ship #1, will 2 catch up with 1.


Homework Equations





The Attempt at a Solution


I solved for the relative velocity of ship 2 in the IRF of ship 1. I got .7143c. I'm not really sure where to proceed from here. Any ideas?
 
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The spaceships move in the same direction, so the relative velocity can't be larger than 0.6c. I don't think it's very useful to compute anyway.

Just compute when and where the spaceships catch up in frame S. This can be done in the classical way. Then use the lorentz transform to find the time in the frame of
ship #1
 

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