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## Main Question or Discussion Point

Hey guys, to further my understanding of special relativity, could you help me out with this problem:

Two spaceships A and B fly directly towards each other. Each has a velocity of magnitude c/4 relative to the Earth, in a direction perpendicular to the line from the Earth to the spaceship. Each is capable of firing a powerful laser beam with frequency, f.

According to an observer on Earth (who receives radio notification of the event), both spaceships fire their lasers directly at each other at the same time.

Who fired first according to an observer in:

a) Spaceship A?

b) Spaceship B?

c) A third spaceship (C), which is travelling in the same direction and with the same speed as A, but which has already passed B?

For a) I said that in A's rest frame, B is coming towards it with speed v=8c/17. So the laser pulse from A will reach B in a time,t1, where B comes to meet the pulse. t1 is shorter than the time B's pulse takes to reach A, since A is not moving relative to the pulse.

Is this logic correct? Any maths to back it up/corrections/help with other parts would help a lot.

Thanks in advance :-)

Two spaceships A and B fly directly towards each other. Each has a velocity of magnitude c/4 relative to the Earth, in a direction perpendicular to the line from the Earth to the spaceship. Each is capable of firing a powerful laser beam with frequency, f.

According to an observer on Earth (who receives radio notification of the event), both spaceships fire their lasers directly at each other at the same time.

Who fired first according to an observer in:

a) Spaceship A?

b) Spaceship B?

c) A third spaceship (C), which is travelling in the same direction and with the same speed as A, but which has already passed B?

For a) I said that in A's rest frame, B is coming towards it with speed v=8c/17. So the laser pulse from A will reach B in a time,t1, where B comes to meet the pulse. t1 is shorter than the time B's pulse takes to reach A, since A is not moving relative to the pulse.

Is this logic correct? Any maths to back it up/corrections/help with other parts would help a lot.

Thanks in advance :-)