An unfortunate astronaut loses his grip during a spacewalk and finds himself floating away from the space station, carrying only a rope and a bag of tools. First he tries to throw a rope to his fellow astronaut, but the rope is too short. In a last ditch effort, the astronaut throws his bag of tools in the direction of his motion, away from the space station. The astronaut has a mass of ?a=102 kg and the bag of tools has a mass of ?b=19.0 kg. If the astronaut is moving away from the space station at ?i=1.20 m/s initially, what is the minimum final speed ?b,f of the bag of tools with respect to the space station that will keep the astronaut from drifting away forever?

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