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

[zeromodz]

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?

 

[kuruman]

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?

 

[Filip Larsen]

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.

 

[Superstring]

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...