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 135 kg and the bag of tools has a mass of 19.0 kg.  If the astronaut is moving away from the space station at 1.50 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

momentum conservation

(135 + 19) x 1.5 = 135 x Va + 19 x Vt

Va = 0

19 x Vt = 231
Vt = 12.15789473684211 m/s <----------minimum final speed of the bag of tools

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