That boy should have been careful

A boy is initially seated on the top of a hemispherical ice mound of radius \(R = 13.8 m\). He begins to slide down the ice, with a negligible initial speed. Approximate the ice as being frictionless. At a height \[\dfrac{a}{b} \times R,\] the boy lose contact with the ice, where \(a\) and \(b\) are coprime positive integers. What is the value of \( a+b\)?

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