A 89.4 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 40.6 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.

It will take the astronaut 239.55 seconds to get to the ship after he has thrown the wrench.

Explanation:

The astronaut and the wrench are an isolated system; therefore, the law of conservation of momentum applies:

,

where, , and are the mass & velocity of the the wrench and he astronaut respectively.

Putting in numbers we get:

which is the velocity of the astronaut.

With this velocity, the time it takes the astronaut to cover a distance of 40.6 will be

Thus, it will take the astronaut 239.55 seconds to get to the ship after he has thrown the wrench.

P.S: we discounted the constant velocity of the ship because the astronaut was at rest relative to it (he was moving at the same velocity)