Question: A single-stage rocket is in deep space coasting at [velocity (rocket, initial)] = 2.5 × 103 m/s. It fires its engine, which has an exhaust speed of [velocity (exhaust)] = 1.3 × 103 m/s.
Part A: What is the rocket's speed [Velocity (rocket, final)] after it has lost one-third of its inertia by exhausting burned fuel?
I need help to solve the above question and assume that the fuel is ejected all at once, and that the exhaust speed is measured relative to the final rocket's speed [velocity (rocket, final)].