Dick places a small ball exactly on the top of a bigger, heavier ball. He simultaneously releases the balls from a height of 1 meter above ground, as shown. He has chosen the masses of the balls so as to maximize the height up to which the smaller ball bounces.

How high above the initial position will the smaller ball bounce up to?

**Assumptions:**

- All collisions are perfectly elastic.
- Air resistance is negligible.
- The figure is not drawn to scale.

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