How Do Two Astronauts Separate in Space After Pushing Each Other Apart?

[cathliccat]

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]

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.

 

[M98Ranger]

First of all, don't feel dumb! Physics and math can be challenging for many people, and it's completely normal to struggle with certain concepts. It's great that you're seeking help and trying to understand the problem more.

To solve this problem, we can use the conservation of momentum equation, which states that the total momentum of a system before and after an interaction remains constant. In this case, the two astronauts are initially at rest, so their total momentum is zero. After they push each other apart, their total momentum is still zero.

Using the formula you mentioned, Xcm = M1X1 + M2X2 / (M1 + M2), we can set up the following equation:

0 = 60(0) + 80(X2) / (60 + 80)

Simplifying this, we get:

0 = 80X2 / 140

We can then solve for X2 by multiplying both sides by 140 and dividing by 80, giving us:

X2 = 0

This means that the heavier astronaut does not move at all, and the lighter astronaut moves 12 meters. So the separation between them is 12 meters.

In general, when solving problems like this, it's important to carefully consider the units and make sure they are consistent throughout the problem. Also, double check your calculations to make sure you haven't made any mistakes. It's always a good idea to go back and check your answer to make sure it makes sense in the context of the problem.

I hope this helps! Keep practicing and seeking help when needed, and you'll get better at these concepts. Don't give up!