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

V = velocity of astronaut + bag initially = 1.20 m/s

Ma = mass of astronaut = 102 kg

Mb = mass of bag = 19 kg

Va = velocity of astronaut after throwing the bag = 0 m/s

Vb = velocity of bag

using conservation of momentum

(Ma + Mb )V = MaVa + MbVb

(102 + 19) (1.20) = 102(0) + 19 Vb

Vb = 7.6 m/s

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