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 113 kg and the bag of tools has a mass of 10.0 kg. If the astronaut is moving away from the space station at 2.10 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? Number m/s

Explanation / Answer

1)

mass of a austronaut, Ma = 113 kg

mass of tool, Mt = 10 kg

combine speed of austronaut and tool is Vo = 2.1 m/s

from conservation of momentum

(Ma + Mt)Vo = MaVa + MtVt

(113 kg + 10 kg)*2.10 m/s = 113(0) + 10*Vt

Vt = 25.83 m/s is the speed of bag tool

2)

from conservation of momentum

2030 x 2.75 = (2030 + 3.05*479) x v

v= 1.60 m/s   

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