Astronaut Bob loses his grip during a spacewalk and finds himself floating away

Question

Astronaut Bob 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 Jane, who is tethered to the space ship, but the rope is too short. In a last ditch effort, Bob throws his bag of tools in the direction of his motion (away from the space station). The astronaut has a mass of 124 kg and the bag of tools has a mass of 13.0 kg. If Bob 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 Bob from drifting away forever?

Explanation / Answer

The astronaut needs to reduce his velocity (and hence momentum) to zero to stop moving away from station.
Using conservation of momentum,
momentum before = (124 + 13)*2.40 = 328.8 mkg/s
momentum after = (124*0+ 13.0*v) = 13.0v
328.8 = 13.0v
v = 328.8/13.0 = 25.3 m/s

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