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 113 kg and the bag of tools has a mass of 13.0 kg. If the astronaut is moving away from the space station at 2.10 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

the astronaut+bag has momentum (113+13.0)*2.1 = 264.6 kg-m/s relative to the station

We want him to have momentum < 0, so he will be drifting back toward the station.

So, the bag must have all the previous momentum.

13.0 * v = 264.6
v = 20.35 m/s

With this bag velocity, the astronaut comes to a halt. Anything greater causes him to drift backwards.