A 87.2 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. The astronaut turns away to look at Earth and several seconds later is 44.2 m behind the ship, at rest relative to the spaceship. The only way to return to the ship without a thruster is to throw a wrench directly away from the ship. The wrench has a mass of 0.411 kg, and the astronaut throws the wrench with a speed of 24.1 m/s.

Question

A 87.2 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. The astronaut turns away to look at Earth and several seconds later is 44.2 m behind the ship, at rest relative to the spaceship. The only way to return to the ship without a thruster is to throw a wrench directly away from the ship. The wrench has a mass of 0.411 kg, and the astronaut throws the wrench with a speed of 24.1 m/s.
How long does it take the astronaut to reachthe ship?
please show the steps

drwls · Answer

He has to close a gap of X = 44.2 m. Use conservation of momentumn to get his velocity relative to the ship, V, after he throws the wrench. 0.411*24.1 = 87.2 * V The time required is X/V.