A 60-kg astronaut is in space, far from any objects that would exert a significa

Question

A 60-kg astronaut is in space, far from any objects that would exert a significant gravitational force on him. He would like to move toward his spaceship, but his jet pack is not functioning. He throws a 720-g socket wrench with a velocity of 5 m/s in a direction away from the ship. After 0.50 s, he throws an 800 g spanner in the same direction with a speed of 8 m/s. After another 9.90 s, he throws a mallet with a speed of 6 m/s in the same direction. The mallet has a mass of 1070 g. How fast is the astronaut moving after he throws the mallet?

Explanation / Answer

It's a conservation of momentum problem. The time intervals between throwing the objects don't matter, just sum the three momentum values:

(0.72 kg)(5 m/s) = 3.6 kg m/s

(0.8 kg)(8 m/s) = 6.4 kg m/s

(1.07 kg)(6 m/s) = 6.42 kg m/s

for a total of 16.42 kg m/s. Divide that by the mass of the astronaut:

(16.42 kg m/s)/(60 kg) = 0.274 m/s

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