Young acrobats are standing still on a circular horizontal platform suspended at the center. The origin of the two-dimensional Cartesian coordinate system is assumed to be at the center of the platform. A 30.0-kg acrobat is located at (3.00 m, 4.00 m), and a 40-kg acrobat is located at (−2.00 m, −2.00 m). Assuming that the acrobats stand still in their positions, where must a 20.0-kg acrobat be located so that the center of mass of the system consisting of the three acrobats is at the origin and the platform is balanced?
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