BRENT ROBERTSON WRITE UP 6- PROBLEMS

In these write ups we had a collection of 11 very interesting problems that involved some applications of some of the math we have proven and or analyzed with the technology this semester. The problem involved an interesting proposition in football where the ball is placed on the side hash mark for a field goal kicker to try to kick though a set of parallel goal posts. The question is, " Are the closer field goals at a disadvantage because the 'window' to the opening is more narrow the closer you get?" Or is there little significant difference in the goal oppening based on how close or how far back the ball is placed. We will use geometry concepts and the getometers sketchpad to get to the bottom of the problem!

First of all we need some definitions of the football field distances and goal post dimensions.

Here is a diagram:

The goal posts have been defined to have a distance of 18.5 feet

With this information, I constructed a sketchpad diagram to look at the angles and see how the measurements changed if at all. The mathemmatics will ultimately expain the result.

SO THE QUESTION REMAINS SHOULD THE TEAM PURPOSELY MOVE THE BALL BACK WHEN THEY GET CLOSE TO GET A BETTER ANGLE AT THE GOAL POSTS?

To answer this question I made a scale model on geometers' sketchpad. The dimensions of a football field fit nicely into a ratio of two to one because the football field is 100 yards across plus two 10 yard endzones for a total of 120 yards. The horizontal distance of sketchpaD IS 60 cm so the unit multiplier was formed 2 yards = 1 cm. Thus the 10 yard increments measured 5 cm, the 120 length was 60 cm and the 53 and one-third yard width converted to 26.67 cm. The other scal measurements were similarly calculated. Here is an example of the scale field:

So now we can begin our investigation. It is important to note that although the sizes have been changed from a collegiate football field, because the figures are similar, the angle measurements will be exactly the same. So we can investigate knowing that these are the exact angles that the bulldog kicker must face in a real UGA game. Here is the angles from the far hash mark and the direct center of the field from the 10 yard line. (Technically th9is is called a 27 yard field goal, but that is another story.

As you can see the far hash mark has a smaller angle 15.99 than the straight shot 17.70. This would indicate that a try from stright on has a greater probablity for success. Now let's see if it is beneficial for a team to purposely move the ball back on the far hash mark to get a better angle. Let'w look at 20 yards out:

So we see that moving a "chip shot" back decreases the angle of success on the far hashmark just as in the dead center of the field. The hashmark kick angle decreased from a 15.99 to an 11.20 and the dicrecdt center decreased from 17.70 to 11.81.

Here is a java file that you can play with to see how the angles are affected as the ball . Well, I actually had a great animation that showed it was more of the ball moving away from the goal posts that reduced the successful angle of approach. I tried to save it as a Java sketch but unfortunately it didn't work and I inadvertanlty did not re save it as an original sketchpad document. So if your rreading this now it means that I had to finish other things rather than redo what I had already done. :-)