How Far Apart Are Two Astronauts After Pushing Off Each Other?

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Homework Help Overview

The problem involves two astronauts in outer space who push off each other, with the goal of determining how far apart they are after the lighter astronaut has moved 5.0 m. The context is rooted in the principles of conservation of momentum.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of conservation of momentum and the implications of the center of mass remaining at rest. Questions arise regarding how to solve for two unknown velocities given the different masses of the astronauts.

Discussion Status

Some participants have offered insights on relating the speeds of the astronauts to their respective distances moved, suggesting that this relationship could help in solving the problem. There is an ongoing exploration of how to express one astronaut's speed in terms of the other's.

Contextual Notes

The discussion highlights the challenge of working with different masses and the initial condition of both astronauts being at rest. There is an emphasis on the need to consider the conservation laws without providing explicit solutions.

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Homework Statement


Two astronauts, one of mass 62 kg and the other 85 kg, are initially at rest in outer space.
They then push each other apart. How far apart are they when the lighter astronaut has moved 5.0 m?


Homework Equations


Conservation of momentum.
Pi = Pf
P1i + P2i = P1f + P2f

The Attempt at a Solution


Pi = Pf
P1i + P2i = P1f + P2f
(62)(0) + (85)(0) = (62)Vf1 + (85)Vf2

How do I solve for 2 unknowns when you can't cancel the masses out because the masses are different?
 
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When momentum is conserved, the center of mass does not accelerate, i.e. it keeps its initial velocity. In this case the velocity of the center of mass is initially zero, so it remains zero after the push. Can you use this information to your advantage?
 
From conservation of momentum you are in this case able to express the speed (with sign) of one astronaut as a function of the speed of the other. Now you should be able to think about how these speeds relate to the distance each astronaut has moved and what that has got to do with the one distance you do know.
 
Because you started at rest, you know that the net velocity is going to be 0. Try plugging in a velocity for the lighter astronaut...
 

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