A 82.6 kg astronaut is working on the engines of a spaceship that is drifting th

Question

A 82.6 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 sec- onds later is 40.3 m behind the ship, at rest relative to the spaceship. The only way to re- turn to the ship without a thruster is to throw a wrench directly away from the ship. The wrench has a mass of 0.405 kg, and the astro- naut throws the wrench with a speed of 18.8 m/s. How long does it take the astronaut to reach the ship? Answer in units of s.

Please show work and explanation

Many thanks

Explanation / Answer

using newton's 3rd law there is an equal and opposite force on each. so momentumod wrench = momentum of astronaut.
Mass wrench x Vw = mass astronaut x Va
0.405 x 18.8 = 82.6x Va
Va = 0.446 x 16.5/85.1 = 0.0921 m/s
time to travel 40.3 m = dist/vel = 40.3/0.0921 = 437.2 s

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