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 the station so there is no way to pull herself back. Fortunately she has a rivet gun used for repair that shoots small metal objects at a high speed.

If she is a distance of 14 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 189 kg, the mass of the rivet is 0.15 kg, and the speed of the rivet leaving the gun is 90 m/s.

Give your answer in seconds to one decimal place.

Explanation / Answer

Since there is no external force, hence we can conserve momentum.

m1u1 + m2u2 = m1v1 + m2v2

here, u1 = u2 = 0

        m1 = 189 kg, m2 = 0.15kg, v2 = 90m/s

thus, 0 = 189v1 + 0.15*90

v1 = - 0.07143 m/s (- sign shows opposite direction)

time taken = D/v = 14/0.07143 = 196 seconds

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