# Linear momentum equation help

I feel pretty dumb, but I can't get the right answer. I'm terrible at basic math concepts, so don't ask me how I managed to get through 2 college math courses and now I'm stuck in physics AND statics.

Anyway my problem is: 'Two astronauts (one mass 60 kg and one mass 80 kg) are initially at rest in outer space. They push each other apart. What is their separation (in m) after the lighter astronaut has moved 12 m round off to the nearest whole number?'

I know that Xcm=M1X1+M2X2/M1+M2 is my formula, my teacher even said so after I asked him. So if 0=60(12)+80x/60+80 = 720+80x/140. That's where I get stuck - I get an answer of 1260 for my second distance which can't be right because it should be less than 12. So I must be doing this REALLY wrong. [b(] Can you help me? I know once I get the answer I need to add that to 12 to get the total amount of their separation. My guess is it should be 17m.

jamesrc
Gold Member
I think you're just having a problem with your parenthesis. Your equation is correct:

(m1+m2)xcm = m1(x1) + m2(x2)

since xcm = 0 and x1 = 12:

0 = 60(12) + 80*x2

x2 = -9 m

The negative sign just indicates that m2 is on the other side of the middle. As a sanity check, you should notice that the center of mass is closer to the heavier one.