The coefficient of restitution

The kinematic equations apply to a bouncing ball.

v2 = u2 + 2as

Manipulation gives at once ... 1/2 mu2 = mgh

Applying this equation to each successive bounce gives ...

1/2 mu12 = mgh1 ... etc.

1/2 mu22 = mgh2 ... etc.

1/2 mu32 = mgh3 ... etc.

At once ...

u1/u2= (h1/h2) 0.5 ... etc.

u2/u3= (h2/h3) 0.5 ... etc.

u3/u4= (h3/h4) 0.5 ... etc.

The ratios, defined as the coefficient of restitution, are found to be constant for many materials.

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