How long does it take for a signal to reach a moving spaceship at 0.866c?

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SUMMARY

The discussion centers on calculating the time it takes for a light signal to reach a spaceship moving at 0.866c from a distance of -4 light seconds. The initial equation used, t=(ΔD)/(c-v), led to an incorrect result of 29 seconds, while a spacetime diagram suggested the correct answer is approximately 12 seconds. The discrepancy arises from the frame of reference and the interpretation of the ship's position at t=0, which is crucial for accurate calculations.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation and simultaneity.
  • Familiarity with the speed of light as a constant (c = 3e8 m/s).
  • Ability to interpret and create spacetime diagrams.
  • Proficiency in rearranging and applying equations related to motion and light signals.
NEXT STEPS
  • Study the implications of the Lorentz transformation in special relativity.
  • Learn how to construct and interpret spacetime diagrams for various scenarios.
  • Explore the concept of simultaneity in different reference frames.
  • Practice solving problems involving relative motion and light signals using the correct equations.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of special relativity and the behavior of light signals in moving reference frames.

vysis
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Homework Statement



A signal (traveling at the speed of light) is sent from -4 ls (light seconds) towards a moving spaceship traveling at 0.866c. How long does it take for the signal to reach the ship?

Homework Equations


I'm pretty sure its t=(delta)D/c-v

But I continue to get the wrong answer with it.


The Attempt at a Solution



using the equation above [rearranged from d(light) = (delta)d + vt]. I get 29 seconds. I do it by multiplying 4 ls by 3e8 and use that as my distance.

according to a spacetime diagram I have, the answer should be around 12s (my diagram might be wrong, but it doesn't seem so). But I can't seem to get it with this equation.
 
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Which way is the ship moving? Where is it at t = 0?
 
the ship is moving in the positive direct and is at 0 ls when t = 0
 
btw, this is all from signal sender's frame of reference.
 
Why do you think your answer is wrong?
vysis said:
I get 29 seconds.
I get a slightly different answer.
 
hm... because I have a spacetime diagram modeling this answer and it seems that it is only supposed to be 12 seconds...
 

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