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A ball is projected from a point on one of two smooth parallel vertical walls toward the other, in a plane perpendicular to both walls. After being reflected at each wall it strikes the second wall at a point in the same horizontal level from which it started. The separation between the walls is a, the free (horizontal) range on level ground would be b, and the coefficient of restitution is e. Which statement is correct?

1. The total time from O to C is (a/(2 u e²)) (e² + e + 1)
2. The free range on the horizontal plane is b = 2uv/g
3. b e² = a (e² + e + 1)
4. All of the above options are correct

Correct answer: All of the above options are correct

Solution

Working through the successive wall reflections (horizontal speed multiplied by e each bounce) and equating total horizontal travel to the geometry reproduces all three relations, so all options are correct.

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