Solve Astronaut Wrench Problem: Find x_2 from x_1, v

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The discussion revolves around solving a physics problem involving an astronaut and a wrench, where the astronaut throws the wrench with speed v while initially at rest at distance x_1 from a spaceship. The key point is that the center of mass (C.M.) of the astronaut-wrench system remains at distance x_1 from the spaceship throughout the motion. Participants express confusion about how to calculate the final distance x_2 after the wrench is thrown, questioning the need to determine x_1 and the change in distance (delta x) first. There is a call for clarity on the calculations involved, with one participant urging others to share their work for better understanding. The conversation highlights the complexities of applying concepts of center of mass in this scenario.
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This problem is driving me insane:
An astronaut is initially at rest, at a distance x_1 from the spaceship. She hurls a wrench with a speed v, relative to the spaceship. Find the final distance x_2 between the spaceship and the wrench using some or all of the variables given.
 

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Only internal forces act upon system astronaut+wrench.
Hence, since the C.M. of this system is at rest relative to the spaceship initially, it (the C.M) will remain at the same position throughout the period.
That is, the C.M of astronaut+wrench will remain at the distance x1 from the spaceship.
 
Aren't they looking for the final distance x_2 after the wrench was thrown? So wouldn't you need to first find x_1 and delta x to find x_2?
 
I'm still not getting the right answer..any other suggestions?
 
I don't know how you're not getting the right answer.
Post your work.
 
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