A 85.1 kg astronaut is working on the en- gines of a spaceship that is drifting

Question

A 85.1 kg astronaut is working on the en-

gines 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 35.4 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 0.446 kg, and the astro-

naut throws the wrench with a speed of 16.5

m/s.

How long does it take the astronaut to reach

the ship?

Answer in units of s.

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
0.446 x 16.5 = 85.1 x Va
Va = 0.446 x 16.5/85.1 = 0.0864 m/s
time to travel 35.4m = dist/vel = 35.4/0.0864 = 409.722 s

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