A classical mechanics problem by my physics teacher

Mass A is released from a height \(h\) on this curved, frictionless curve. Mass A will hit mass B and the two will stick together and continue traveling from left to right up the curve. What will be the maximum height of combined masses A and B on the right side of the curve? If the answer can be written in the form \(\dfrac{a}{b}h\) (simplest form), find \(a+b\).

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