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)

First I want to poke holes in the semantics of this problem. How did he get 34.0 m behind the ship? Did he experience some sort of freak teleportation? If the ship is moving, this cannot be answered without knowing the speed of the ship. Should we assume that several seconds mean two? three?

Okay, now that I've gotten that out of my system, the answer is a simple matter of momentum. If we assume that the ship is also at rest relative to him (which we must, otherwise this problem is unsolvable as described,) then the momentum of the wrench must be equal to the momentum of the astronaut after the wrench has been thrown.

We will use m₁ is the mass of the wrench, m₂ is the mass of the astronaut, v₁ is the speed at which the wrench is thrown and v₂ is the speed at which the astronaut will travel towards the space ship.

Due to conservation of momentum, m₁v₁ = m₂v₂ Therefore the Astronaut's speed = v₂ = m₁v₁/m₂

It will take the astronaut d/v₂ seconds to reach the space ship.

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