Coefficient of restitution of a ball question

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The coefficient of restitution (COR) of a ball is independent of the height from which it is dropped due to the principles of energy conservation and the nature of elastic collisions. As the ball falls, it accelerates until it reaches terminal velocity, at which point the speed of impact remains constant regardless of the drop height. This phenomenon occurs because, beyond a certain height, the energy lost to deformation during the collision becomes negligible, leading to a consistent COR value across various heights.

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Jeven
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Why is the coefficient of restitution of a ball independent of the height it is dropped from?

A mathematical explanation would be best. Thank you.
 
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I suppose is just an approximation, for deformations within some limits.
Besides, for heights larger than some limit, the ball reaches terminal speed in free fall and the collision speed does not change after that.
But some context will help.
 

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