Two space craft are flying towards a planet

[pat666]

Homework Statement

Two spacecraft are flying towards a planet at 0.9c and 0.3c relative to the planet, respectively. If they fire their laser beams simultaneously from a range of 109 m, which will strike the planet first and what will be the delay before the other beam strikes?

Homework Equations

The Attempt at a Solution

Einstiens 2nd postulate: The speed of light in a vacuum is completely independent of the motion of the source emitting it.

From that it seemed to me that the laser's would hit the planet at the same time...then I started considering length contraction, if the 109m was measured from the planet then there "actual" distances would be different resulting in a delay. Admittedly I have a terrible grasp of this topic so this could be complete bs. The question wording I think is pretty bad (could just be me) so I need someone with a better understanding to read it and give me a clue about considering length contraction (necessary or not??).
thanks for any help!

 

[CompuChip]

The key word here is "simultaneously".
Assuming that they mean that they both fire at the moment that the ships are 109 m away from the planet, in the rest frame of the planet, I would say you are right: they hit at the same moment because each light beam takes the same time to cover that distance.

However, if they mean that the ships fire the laser beam at the moment that each of them measures their own distance to the planet to be 109 m, then one light beam will arrive later (I think) because they don't fire simultaneously.

So I am inclined to agree with you that there is a "problem" in the question, namely that they didn't specify in which of the three frames (planet, spaceship 1 or spaceship 2) the lasers are fired simultaneously.

 

[pat666]

Thanks compuchip,
This is for an assignment so I'm wondering which way you would go?

 

[CompuChip]

I would go my professor's way and ask him what he means, arguing why you think the answer is "they arrive at the same time" and that you doubt he meant it to be that trivial.

 

[pat666]

ok thanks