Relativity and Simultaneity in Laser Beam Strikes

[ProPatto16]

Relativity, Trick Question??

Homework Statement

Two Space Craft 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 10^9m, which will strike the planet first and what will be the delay before the other beam strikes?

Homework Equations

Ua = (Ub + v)/(1+Ub*v/c^2)
Ua = speed of beam relative to planet
Ub = spped of beam relative to ship
v = speed of ship relative to earth
c = speed of light

The Attempt at a Solution

A laser beam is just light isn't it? I am sure it is. even more so since there's no values for speed of beam. but if speed of beam is c then Ua = Ub since c is the same in all reference frames.
Then since the beams are fired simultaneously from equal distance, and they're equal speed, they should hit at the same time

Also, using formula and letting Ub = c, then Ua = c.

so beams hit at the same time and there is not time before other beam strikes.

It just seems strange to me that they write up a question like this and its really really simple, its not very often you see numbers in questions that arent relevant. so i just automatically doubt myself.

Opinions?

 

[Doc Al]

The problem is ambiguously worded. The lasers fire simultaneously according to whom? At a range of 10^9m according to whom?

If they fired simultaneously from the same distance according to planetary observers (say), then your answer is correct: of course they hit the planet at the same time.

 

[ProPatto16]

Thats exactly the thought i had, but it doesn't specify either, and since the question is set in the planets reference frame then one would assume that its in the planets reference frame at which the beams are fired simultaneously.
And it gives no position of either spacecraft relative to Earth or each other. So even if it were a proper question there isn't enough information to solve it mathematically anyway.