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Physics question HELP?

A 84.7 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 34.0 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 0.450 kg, and the astro-

naut throws the wrench with a speed of 24.6

m/s.

How long does it take the astronaut to reach

the ship?

Answer in units of s.

Answers (2)

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this problem requires equations relating to the conservation of momentum.

M1 x V1 = M2 x V2

84.7 x V1 = 0.45 x 24.6

84.7 x V1 = 11.07

V1 = 0.1307 m/s

34 / 0.1307 = 260.14 seconds