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 11 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 133 kg, the mass of the rivet is 0.04 kg, and the speed of the rivet leaving the gun is 130 m/s. Give your answer in seconds to at least three significant digits. Do not include units in your answer. You will not be graded on the number of significant digits, this is just to avoid having your answer counted as incorrect due to rounding errors.

Explanation / Answer

Let’s use the following equation to determine her speed.

Force * time = mass * change of velocity

Since the force and time are constant, the product the mass and change of velocity are constant.

m1 * v1 = m2 * v2

133 * v1 = 0.04 * 130

v1 = 0.039 m/s

This is approximately 0.039 m/s.

now distance = velocity * time

d = v * t

11 = 0.039 * t

t = 11 / 0.039 = 282.05 sec

This is approximately 282 seconds. so her take 282 seconds to get back.

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