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Rapidly spinning elastic rubber ball was released from rest at height 5 meter above the floor ?

The ball experiences absolutely elastic bounce off the floor, and continues to bounce, leaving black marks at the spots of each bounce.

What is the distance between the first and the second mark?
Friction between the ball and the floor is μ=0.5, g=10m/s².

When the ball bounces, it will skid resulting in only kinetic friction. The normal reaction will be in the form of an impulse, and so will the frictional force which will give the ball a horizontal component of velocity.

Its vertical velocity before impact is √(10g) = 10 m/s. Its velocity after impact is 10 m/s as well (assuming this is what "absolutely" elastic means).

This means the impact reaction force results in a momentum change of 20*M units. The frictional force then results in a momentum change of 0.5 * 20M = 10M units. I.E. the horizontal component of velocity after impact is also 10 m/s.

So it rebounds at a 45 deg angle with velocity 10√2 m/s. The range of travel is 20 m.

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