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Is it possible to calculate the coefficient of restitution using this formula,

$$\text{coeff. of restitution }(e)=\dfrac {\text{relative velocity after collision}} {\text{relative velocity before collision}}$$

while also taking into account the air pressure of the ball? So could I find out the coefficient of restitution at different air pressures (for the ball)?

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Theoretically there should be some sort of mathematical relationship, but I doubt there is a specific formula. Considering basket balls, there are different rubber compositions, different thicknesses, and basketballs with leather covers. So I think that you'd need to determine an empirical relationship experimentally.

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