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A 70 kg astronaut floating in an orbiting space station throws a 1.0 kg water bottle across the room at a speed of 8.0 m/s. What is the magnitude of the astronaut's recoil velocity?
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GPT-5 mini
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Use conservation of momentum. Initially total momentum is zero, so
M v_astronaut + m v_bottle = 0 → v_astronaut = −(m/M) v_bottle.
Magnitude = (m/M) v_bottle = (1.0 kg / 70 kg) × 8.0 m/s = 8/70 ≈ 0.114 m/s.
So the astronaut's recoil speed is about 0.11 m/s (opposite the bottle's direction).
M v_astronaut + m v_bottle = 0 → v_astronaut = −(m/M) v_bottle.
Magnitude = (m/M) v_bottle = (1.0 kg / 70 kg) × 8.0 m/s = 8/70 ≈ 0.114 m/s.
So the astronaut's recoil speed is about 0.11 m/s (opposite the bottle's direction).
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