As a football is passed through air it follows a curve.  This curve is called a parabolic path.  This path is caused by the influence of gravity while the ball is in the vertical direction.  Gravity stops the ball for a second at it's peak height, then the ball accelerates downward causing the parabolic arc.  Projectile motion of the ball is the technical name for the path of any object that is launched or thrown.  When a quarterback releases the ball he can control the velocity and the rotation of the ball.   The rotation of the ball  influence how the ball slows down in flight because the football is affected by air drag.  A spriling football will have less air drag then a end over end pass.  This will let it stay in the air longer and go a much further distance.  The three factors a quarterback can add to a football to change it's destination is Force, Velocity, and angle of the ball.
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