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Suppose I have a tennis ball of COR 0.5. This means that when it bounces on an immovable object (like a floor), then it will return with 0.5x the velocity, right?

Now suppose I also have a football of COR 0.8. If I bounce the tennis ball on the football, how much energy will be lost? Say the football is on the ground and I drop the tennis ball from a height of 1m, how high will it bounce (assuming that it bounces straight up)?

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Assuming that the COR remains constant for the velocity range, it's a simple multiplication for subsequent bounces: $$v_{i+1} = \epsilon\cdot v_i$$ or resolved for the COR $$\epsilon = \frac{v_{i+1}}{v_i}$$. Remember that $E_{kin} \propto v^2$ and you see that the ratio of kinetic energy is the square of the COR (mass stays constant so cancels out)

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Like the coefficient of friction, the coefficient of restitution is an empirical quantity and it relates to the pair of objects which collide, not to only one of these objects. If one object in the pair is very much more deformable than the other, the COR when that object collides with other non-deformable objects of the same shape might be approximately the same.

For a ball bouncing on a solid plane surface the COR depends on the material and structure of the ball and the plane surface, and internal pressure if the ball is inflated.

For these reasons it is not possible to calculate the unknown COR of one pair of objects from the known CORs of other pairs. So if as here you know the COR for combinations AB and AC it is not possible to deduce the COR for BC.

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