Assignment 6:  Field Goal Problem


Jonathan Sabo

The football rules in college football were changed a few years ago have made the uprights 5 feet narrower than previously. Many game commentators have harped about how much harder it is to kick field goals from the hash marks. Assume the field goal is attempted from the hash marks. At what yard marker does the kicker have maximum angle to the two uprights. Note: You will need to find out the width of the uprights and the width of the hash marks . . . make a sketchpad model. Is there any merit to some commentators argument to take a penalty in order to have a "better angle" on the field goal kick?

The first thing needed for this exploration is the dimentions of a NCAA football field.  By doing an internet search I was able to find the appropriate information for this exploration.  
Using this information I was able to construct a NCAA football field using Geometer's SketchPad.  

This picture is drawn to scale of a NCAA football field.  Point F represents the right side of the goal posts and point G represents the left side of the goal posts.  Point B represents where the ball is located.  If you would like to manipulate the location of the ball you can use this GSP file.  If you drag point B, the angle to the uprights will change.  After manipulating the points we find that the largest angle to the goal posts is actually in the end zone.  When the ball is 5.82 yards away from the goal posts the anlge between the ball and the goal posts is .  However it is not realistic to kick a field goal from inside of the end zone.  In college football, field goals are attempted from seven yards behind the line of scrimmage.  Therefore, the largest realistic angle would be from the seven yard line.  At this discance the angle between the ball and the goal posts is approximately .  As the ball moves further away from the goal posts the angle gets smaller and smaller. Based on this information it would make no sense to take a penalty to get a better angle at the field goal.  If the ball is moved further away from the goal line the angle to the goal posts will be smaller.  

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