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 Heading
 
  Heading a ball is a really important skill to learn in order to control the ball falling down towards to a player. When a person is heading a ball, the same physics applied to the ball as when it was kicked. The collision is the last process of heading a ball, this also happens in kicking the ball, however it is easier to demonstrate when viewing the physics viewpoint from heading a ball.

  The Elastic Collision
 - - When a ball is kicked by a player and it is traveling through the air, soccer players get a little competition to get it first by heading the ball. As shown in previous page, when a player kicks the center or off-center of the ball, the ball comes with certain velocity and acceleration. The law of conservation of energy is always applied. There will always be the air drag force that acts on the opposite direction of the path of the ball. The ball will be spinning and curving at the same time if the player kicked the off-center of the ball, because of the Bernoulli's principal and Magnus effect. When a player heads the ball, and elastic collision happens. What is the elastic collision? The elastic collision is when the total kinetic energy of two objects before a collision is equal to the total kinetic energy of the two objects after the collision. So the total kinetic energy before the ball hits someone's head is equal to the total kinetic energy after the collision. When the ball hits a person's head when the head is at rest, some of the momentum energy in the ball is transferred to the head. That is why the head has to move back when the ball hits the head, thus the ball will change direction with a certain angle when it comes in contact with the head (as you can see in the equation). That is why the players are heading towards the ball so they also can transfer the momentum energy to the ball in order to accelerate or maintain the speed of the ball (Usually the purpose of heading is to change the direction of the ball with the same velocity. So sometimes there's a situation when a player doesn't need to accelerate the speed of the ball by heading but maintain it by heading towards the ball with acceleration, so the total momentum energy remains in the ball).  

Conservation of momentum
\,\! m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1} + m_{2}v_{2}.

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  Summary of Bibliography


  http://en.wikipedia.org/wiki/Elastic_collision Wikipedia

  The Science of Soccer by author Wesson, John


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