Bounce it like Beckham

Classical Mechanics Level 5

A kid kicks a ball to the wall so that it rolls without slipping. After the collision with the wall, the ball will jump/kick up and make an angle with the ground. Estimate that angle in degrees, if the coefficient of friction between the ball and the wall is very high.

Details and assumptions

  • Assume that the friction between the wall and the ball \(k\) is very high, i.e. \(k\gg 1\). Therefore very, very rapidly in any collision one can treat the ball as rolling without slipping.
  • Treat the ball as a solid sphere with a uniform mass distribution.
  • The collision in the horizontal direction is perfectly elastic, so after the collision the horizontal velocity of the ball is \(-v\) (same magnitude as initial velocity, but opposite direction).

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