It is possible for the velocity of a rocket to be greater than the exhaust velocity of the gases it ejects. When that is the case, the gas velocity and momentum are in the same direction as the rocket's. How does the rocket still obtain thrust by ejecting the gases?

Question

Before the gas was ejected it had a larger momentum in the direction the rocket is moving. But total momentum is conserved. This means that the speed of the rocket must increase.

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