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.