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Consider if I have 3 objects at rest in space: a rocket A and two ejectable pods B and C where the mass of B < mass of C. I want to eject pods B and C (both at speed v0 so that rocket A will move in the opposite direction. The question is whether ejecting B then C OR C then B OR both at same time will result in greatest final velocity of rocket.

If I first eject B and apply the conservation of momentum to B and A + C together, I can then find the resulting speed of A and C together. Then I eject pod C. My question is, can I redefine the system to now be just A and C? Thus can I find the final velocity of A after ejecting C by setting the intial momentum of A and C moving together = final momentum of A + final momentum of C after ejection?

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Yes -- if A and C are no longer interacting with B, then the momentum of the A+C system is separately conserved.

(For example, you could consider momentum conservation of the full system, but then you would realize that since B's velocity does not change when you eject C, it contributes the same momentum to both sides of your equation.)

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