Relative length and velocities using Lorentz transformations

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SUMMARY

The discussion centers on calculating the relative velocities and time intervals of two spaceships, A and B, each with a proper length of 100m, using Lorentz transformations. The time taken for the front end of ship B to pass ship A is given as 1.5 x 10-6 seconds. Participants explore the application of the Lorentz transformation for velocity addition to derive the relative velocity and time intervals from the perspective of both ships. The challenge lies in determining the velocities without initial values, emphasizing the need for understanding Lorentz contraction and proper length in different reference frames.

PREREQUISITES
  • Understanding of Lorentz transformations
  • Familiarity with proper length and time dilation concepts
  • Knowledge of velocity addition in special relativity
  • Basic proficiency in solving physics problems involving relative motion
NEXT STEPS
  • Study Lorentz transformation equations in detail
  • Learn about proper length and its implications in special relativity
  • Research velocity addition formulas in the context of special relativity
  • Practice problems involving time dilation and length contraction
USEFUL FOR

Students of physics, particularly those studying special relativity, educators teaching these concepts, and anyone interested in understanding the implications of relative motion in high-speed scenarios.

clayton26
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Homework Statement


Space ships A and B, each having a proper length of 100m, pass each other moving in opposite directions. According to the clocks on ship A, the front end of B takes 1.5 x 10^(-6) s to pass the entire length of A.

a) what is the relative velocity of the two ships?

b) according to clocks on ship B, how long does it take for the front end of A to pass the entire length of ship B?

c) according to clocks on ship B, how much time passes between the time when the front end of A passes the front end of B and the time when the rear end of A passes the front end of B? Does this time interval agree with your answer to B? Should it?


Homework Equations


Lorentz matrices.


ATTEMPTS:

So here's what's confusing me: I want to apply the lorentz transformation of velocity addition to find the relative velocity of the spaceships, however I'm not sure how to do that since I don't know their respective velocities to begin with. Is there some way to derive the velocity of one or both of the ships given the time it takes for the front end of ship A to pass through the length of ship B? I wanted to simply take delta(x)/delta(t), but I don't know what to use for delta(x) since the problem only gives me the proper length and no velocity to apply a lorentz contraction. So any help with any part of this problem would be greatly appreciated!
 
Physics news on Phys.org
What's the length of ship A in ship A's frame? That's the distance the front end of B travels in the 1.5 μs.
 

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