Kicking the Ball

Kicking is fundamental to soccer. It is informative to analyze a soccer kick using physics. The schematic below illustrates a kick in action. 

 

To analyze the kick we can treat it as an inelastic collision in one dimension, between soccer ball and foot. For inelastic collisions there exists an equation which accounts for the inelastic nature of the collision. This equation relates the initial and final velocities of the colliding bodies. The equation is: 

 

Where: 

e is the coefficient of restitution. For all collisions this value is between 0 and 1. For e = 1 the collision is elastic and kinetic energy is conserved (the most efficient case). For e = 0 the collision is plastic (the most inefficient case), and the colliding bodies stick together and move with the same velocity, after impact 

• V_b1 is the velocity of the soccer ball before the kick 

• V_f1 is the velocity of the foot before the kick 

• V_b2 is the velocity of the soccer ball after the kick 

• V_f2 is the velocity of the foot after the kick