# Stones, Up and Down

From an elevated point $$A$$, a stone is projected vertically upwards. When the stone reaches a distance $$h$$ below $$A$$, its velocity is double of what it was at a height $$h$$ above $$A$$. If the greatest height attained by the stone is $$\frac{ph}{q}$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

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