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31.1: The Coefficient of Restitution
https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/31%3A_Collisions/31.01%3A_The_Coefficient_of_Restitution
By conservation of energy, the kinetic energy of the body just before it hits the floor is $m v_{i}^{2} / 2=m g h_{i}$ , so its velocity is $v_{i}=\sqrt{2 g h_{i}}$ . The coefficient of restitution ...By conservation of energy, the kinetic energy of the body just before it hits the floor is $m v_{i}^{2} / 2=m g h_{i}$ , so its velocity is $v_{i}=\sqrt{2 g h_{i}}$ . The coefficient of restitution is just the square root of the ratio of the rebound height to the initial height. ${ }^{1}$

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