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

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SUMMARY

The discussion focuses on the physics problem involving two astronauts with masses of 62 kg and 85 kg who push off each other in space. Using the principle of conservation of momentum, the initial momentum is zero, leading to the equation (62)Vf1 + (85)Vf2 = 0. By expressing the velocity of one astronaut in terms of the other, the relationship between their speeds and the distances they travel can be established. When the lighter astronaut moves 5.0 m, the distance between them can be calculated using their respective velocities.

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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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