An 80.0-kg astronaut is working on the engines of his
ship, which is drifting through space with a constant velocity.
The astronaut, wishing to get a better view of the
Universe, pushes against the ship and much later finds
himself 30.0 m behind the ship and at rest with respect
to it. Without a thruster, the only way to return to the
ship is to throw his 0.500-kg wrench directly away from
the ship. If he throws the wrench with a speed of
20.0 m/s relative to the ship, how long does it take the
astronaut to reach the ship?

Question

An 80.0-kg astronaut is working on the engines of his
ship, which is drifting through space with a constant velocity.
The astronaut, wishing to get a better view of the
Universe, pushes against the ship and much later finds
himself 30.0 m behind the ship and at rest with respect
to it. Without a thruster, the only way to return to the
ship is to throw his 0.500-kg wrench directly away from
the ship. If he throws the wrench with a speed of
20.0 m/s relative to the ship, how long does it take the
astronaut to reach the ship?

anonymous · Answer

$$M_{wrench} \times Speed_{wrench}+M_{astronaut} \times Speed_{astronaut}=0$$
With this you can calculate the speed of the astronaut versus the ship once he has thrown the wrench. The negative value you get meaning that the velocity of the astronaut has opposite direction to the velocity of the wrench, which means the astronaut starts to move towards the ship. Anyway, I would not recommend this method to NASA

anonymous · Answer

Basically because in outer space there are no hardware stores where astronauts may get a spare wrench

anonymous · Answer

wow thats great! Thanks!

anonymous · Answer

Let x m/s be the final speed of astronaut. Then, by conservation of momentum, 
80x - .5*20 = 0 (Assuming the direction of movement of wrench as negative)
x = 1/8 m/s

Hence,  to cover a distance of 30 m, time taken =  distance/speed = 30*8 = 240 s.