An astronaut floating outside of the International Space Station without a jet p

Question

An astronaut floating outside of the International Space Station without a jet pack has become disconnected from her lifeline so there is no quick way to get herself back to the station. Fortunately she has a rivet gun used for equipment repair that shoots small metal objects at a high speed.

If she is a distance of 10 m from the station, how long will take her to get back if she shoots her last rivet in the direction directly away from the station? Her mass, with space suit, is 144 kg, the mass of the rivet is 0.02 kg, and the speed of the rivet leaving the gun is 120 m/s.

Give your answer in seconds to at least three significant digits.

Explanation / Answer

Momentum of the rivet = 0.02 * 120   = 2.5 kg.m/sec

For the astronaut, momentum   = 144v

=>   144v = 2.5

=> v = 0.01736 m/sec

=>    time will take her to get back = (10 m)/ (0.01736 m/sec)

                                                       = 576.036 sec

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