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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