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

AI Thread Summary
A signal traveling at the speed of light is sent from -4 light seconds towards a spaceship moving at 0.866c. The initial calculation using the equation t=(delta)D/c-v resulted in 29 seconds, but this conflicts with a spacetime diagram suggesting the time should be around 12 seconds. The confusion arises from the reference frame and the ship's position at t=0, which is at 0 light seconds and moving in the positive direction. Participants are trying to reconcile their calculations with the spacetime diagram. The discussion highlights the complexities of relativistic calculations and the importance of correctly interpreting 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... becuase I have a spacetime diagram modeling this answer and it seems that it is only supposed to be 12 seconds...
 

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