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=113 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?

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=113 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?