A 84.5 kg astronaut is working on the engines of a spaceship that is drifting th

Question

A 84.5 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 38.9 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 0.613 kg, and the astronaut throws the wrench with a speed of 24.9 m/s. How long does it take the astronaut to reach the ship? Answer in units of s.

Explanation / Answer

Given Quantities,

Mass = M = 84.5kg, let, velocity

Wrench mass = m = 0.613 kg and speed = v = 24.9 m/s

Distance covered by astronaut = d = 38.9m

Applying Newton's third law of motion, that there is a equal and opposite force on each other. So,

mometum of the wrench = momentum of the astronaut

p = mv (product of mass and velocity)

0.613 x 24.9 = 84.5 x V So we get,

V = .180 m/s

t = d/V =

So we get Time = 216.1 seconds

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