An unfortunate astronaut loses his grip during a spacewalk and finds himself flo

Question

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 102 kg and the bag of tools has a mass of 19.0 kg. If the astronaut is moving away from the space station at 1.20 m/s initially, what is the minimum final speed of the bag of tools (with respect to the space station) that will keep the astronaut from drifting away forever?

Explanation / Answer

The astronaut and the bag has a momentum = Mv = (124+19)*2.10

        = 300.3 kg m/s

when the bag will have all the momentum, the astronaut will come to a halt and will not drift back

19V = 300.3

V = 15.8 m/s

so minimum final speed of bag of tools is 15.8 m/s . anything greater will cause the bag to drift

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