Problem a single stage rocket is in deep space coasting at, Ask an Expert

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Problem: A single stage rocket is in deep space coasting at an initial velocity of 2.5E3 m/s. it fires its engine which has an exhaust speed of 1E3 m/s.

Part A: What is the rocket's final speed after losing 1/3 of its inertia by exhausting burned fuel?

I need tutor help to solve the above problem and assume that the fuel is ejected all at once, and that the exhaust speed is measured relative to the rocket's final speed.

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