Bouncing hard

Two elastic balls of masses m 1 m_1 and m 2 m_2 are placed on top of each other (with a small gap between them) and then dropped onto the ground. What is the ratio m 1 m 2 \dfrac{m_1}{m_2} , for which the upper ball ultimately receives the largest possible fraction of total energy?

Submit your answer to 3 decimal places.

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The answer is 0.333.

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