The Physics Behind A Kick
Here is a diagram depicting how a soccer player kicks a ball. Photo from outstepandinstepbiomechanics.weebly.com, taken from Luhtanen.
Here is a diagram depicting the different forces acting on the ball, including the rotation that the ball experiences. Photo from NASA.
Here is a force diagram depicting the forces that are done upon a soccer ball during a kick.
This is a diagram depicting the parabolic nature of a soccer ball kick. Photo from ck12.org.
This diagram depicts the projectile motion of a soccer ball in greater detail, showing the varying velocities at different heights and range values. It is a common diagram used in many physics textbooks.
When a soccer ball is kicked, your leg puts kinetic energy into the ball. So, beforehand, the ball holds potential energy, and the kinetic energy is transferred from the leg into the ball.
In terms of KE = 1/2mv^2, Kinetic energy is equal to half of the mass of the leg times the square of the velocity of the leg.
In addition to the kinetic energy that is being transferred from the leg into the ball, the ball is also being slightly deformed by your leg. Therefore, the energy going into the collision between the foot and the stored energy inside the ball is equal to the energy coming out as kinetic energy plus heat.
The formula for the velocity of the ball, taking into consideration the deformation of the ball, is
Vball = Vleg(Mleg/(Mleg + Mball))(1+x), where x is the coefficient of restitution, measuring what speed a ball bounces up at compared to the speed it hits the ground on the way down (0 being the ball doesn't bounce at all, and 1 being the ball bounces to the same height every time).
In terms of KE = 1/2mv^2, Kinetic energy is equal to half of the mass of the leg times the square of the velocity of the leg.
In addition to the kinetic energy that is being transferred from the leg into the ball, the ball is also being slightly deformed by your leg. Therefore, the energy going into the collision between the foot and the stored energy inside the ball is equal to the energy coming out as kinetic energy plus heat.
The formula for the velocity of the ball, taking into consideration the deformation of the ball, is
Vball = Vleg(Mleg/(Mleg + Mball))(1+x), where x is the coefficient of restitution, measuring what speed a ball bounces up at compared to the speed it hits the ground on the way down (0 being the ball doesn't bounce at all, and 1 being the ball bounces to the same height every time).