A ball of mass \(m\) is dropped from a height \(h_1\), and after striking the ground the ball bounces back to a height \(h_2\) (\(h_1>h_2\)).

At a height \(h=\frac12 h_2\), the ratio of the kinetic energy during the initial drop to that during the bounce is 2:1, what is the ratio of \(h_1:h_2\)?

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