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

[vysis]

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.

 

[Doc Al]

Which way is the ship moving? Where is it at t = 0?

 

[vysis]

the ship is moving in the positive direct and is at 0 ls when t = 0

 

[vysis]

btw, this is all from signal sender's frame of reference.

 

[Doc Al]

Why do you think your answer is wrong?

I get 29 seconds.

I get a slightly different answer.

 

[vysis]

hm... because I have a spacetime diagram modeling this answer and it seems that it is only supposed to be 12 seconds...