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 10.0 kg. If the astronaut is moving away from the space station at 2.40 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?

Answer 1

You need apply the momentum conservation for resolve this problem.

First you know that astronaut has a mass 102 kg and his velocity with the bag is 2.4 m/s before throw the bag. you know the mass of the bag which is 10 kg. Then you can apply the momentum conservation

where m₁ is the mass astronaut and m₂ is mass bag. And the velocity v₁ is the velocity of the astronaut and v₂ is the velocity bag

The velocity the astronaut and the bag is 2.4 m/s before throw its bag, and for keep the astronaut from drifting away forever his velocity must be zero, then we have the following

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