An astronaut is adrift in space with his spaceship moving away.
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An astronaut is adrift in space with his spaceship moving away. Before it gets out of reach, he needs to catch up to it. He has a bag of 9 rocks, each about 25% of his mass.
When he throws the first rock, he gains a speed of 1 m/s. He throws each successive rock with the same speed (relative to his speed before the throw) gaining speed on each throw.
After the 8th rock is thrown, he has the same velocity as the vehicle. After finally throwing the last rock, how fast is he moving towards the spaceship?
**MCQ
Show answer & explanation
Using conservation of momentum for rocket/reaction propulsion, throwing the final 9th rock with reduced remaining astronaut mass imparts 2 m/s relative velocity.
Step-by-step Derivation:
Step 1: Conservation of momentum: m_astronaut * delta_v = m_rock * v_exhaust.
Step 2: With fewer rocks in the bag, total mass decreases, increasing delta_v per throw.
Step 3: Evaluating the 9th throw velocity increment gives 2 m/s.