Goldilocks And The Three Spheres

Three masses joined by elastic, inextensible strings that initially form an equilateral triangle. Mass A is given velocity \(v_0\) parallel to side \(\overline{BC}\). Eventually mass C starts to move with speed \(v = xv_0/y\), where \(x\) and \(y\) are co-prime positive integers.

Find \(x+y\).

Details and Assumptions:

  • The stings are initially taut.
  • The masses of A, B, and C are in the ratio \(1 : 2 : 3\).

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