CENTER OF MASS: finding final position of skater 3 given final positions of others

Homework Statement

Three ice skaters are on a perfectly smooth frictionless lake. They are together at rest at the middle of the lake when they push off on each other. When skater #1 (m1 = 80 kg) is 6.00 meters EAST of the starting position, and skater #2 (m2 = 60 kg) is 6.00 meters NORTH of the starting position, how far away is skater #3 (m3 = 40) kg from the starting position?

My first intuition was to solve it this way:

Xcom = ((80kg)(6m)+(60kg)(6m) + (40kg)(X3))/180 kg

If I set Xcom to zero, X3 = 3m. Is it that simple?
However, I think I need to break it apart into components, but I'm still unclear about how to do this.

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Doc Al
Mentor

However, I think I need to break it apart into components, but I'm still unclear about how to do this.
Yes, treat the x (East) and y (North) components separately. What are the x and y components of the position of masses #1 and #2?

Xcom = ((80kg)(+6m) + [STRIKE](60kg)(0m)[/STRIKE] + (40kg)(X3))/180 kg

Ycom = ([STRIKE](80kg)(0m)[/STRIKE] + (60kg)(+6m) + (40kg)(X3))/180 kg

Where do I go from here?

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Doc Al
Mentor

Xcom = ((80kg)(+6m) + [STRIKE](60kg)(0m)[/STRIKE] + (40kg)(X3))/180 kg

Ycom = ([STRIKE](80kg)(0m)[/STRIKE] + (60kg)(+6m) + (40kg)(X3))/180 kg
Good.
Where do I go from here?

Also, I tried again by setting Xcom to zero (point of origin),
That's exactly what you're supposed to do.
and solving for it that way, got X=3m.
Show how you got that.

Doc,

I didn't find X3=3m by breaking it up into components. I found X3 by setting Xcom = 0 = ((80kg)(6m)+(60kg)(6m)+(40kg)(X3))/180kg in my original format and solving for it algebraically.

But if I break it into components and set Xcom and Ycom to zero:

Xcom=0= ((80kg)(6m) + 0 + (40kg)(X3))/180
I get..Xx3= -12 m

Ycom=0=((0 + (60kg)(6m) + (40kg)(X3))/180
I get..Xy3 = -9 m

I'm missing the point.

Doc Al
Mentor

Doc,

I didn't find X3=3m by breaking it up into components. I found X3 by setting Xcom = 0 = ((80kg)(6m)+(60kg)(6m)+(40kg)(X3))/180kg in my original format and solving for it algebraically.
Your original approach is incorrect, since it mixes up the x and y coordinates.

But if I break it into components and set Xcom and Ycom to zero:

Xcom=0= ((80kg)(6m) + 0 + (40kg)(X3))/180
I get..Xx3= -12 m

Ycom=0=((0 + (60kg)(6m) + (40kg)(X3))/180
I get..Xy3 = -9 m
Good! You've just found the position coordinates of mass #3:

(X3, Y3) = (-12, -9)

I'm missing the point.
Use those coordinates to find its distance from the starting point.

Thank you very much Doc!