Scoring on a Soccer Goal from Different Positions

by Channing Pezet

Submitted : Spring 2016

A semi circle of radius 20 yards with the center of the goal being the center will be created. There will be seven positions along the semicircle that a player can shoot from, the first and last of these being positions that correspond to the smallest possible area of goal that is possible to score from. Each position will yield a different area of goal to score from giving the players a larger target at certain positions. The smaller the area of goal to score on means the smaller area on the ball the player must strike in order to place the ball in the goal. By finding the different areas on the ball and their corresponding positions a parabola will be created and the derivative of the function of the parabola will be found. The critical point will represent where the ball should be optimally shot from in order to have the largest area of the ball to strike, producing more goals throughout the season.

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