MCM: The Mathematical Contest in Modeling
ICM: The Interdisciplinary Contest in Modeling
PROBLEM A:The Sweet Spot
Explain the ï¿½sweet spotï¿½ on a baseball bat.
Every hitter knows that there is a spot on the fat part of a baseball bat where maximum
power is transferred to the ball when hit. Why isnï¿½t this spot at the end of the bat? A
simple explanation based on torque might seem to identify the end of the bat as the sweet
spot, but this is known to be empirically incorrect. Develop a model that helps explain
this empirical finding.
Some players believe that ï¿½corkingï¿½ a bat (hollowing out a cylinder in the head of the bat
and filling it with cork or rubber, then replacing a wood cap) enhances the ï¿½sweet spotï¿½
effect. Augment your model to confirm or deny this effect. Does this explain why Major
League Baseball prohibits ï¿½corkingï¿½?
Does the material out of which the bat is constructed matter? That is, does this model
predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is
this why Major League Baseball prohibits metal bats?
In 1981 Peter Sutcliffe was convicted of thirteen murders and subjecting a number of
other people to vicious attacks. One of the methods used to narrow the search for Mr.
Sutcliffe was to find a ï¿½center of massï¿½ of the locations of the attacks. In the end, the
suspect happened to live in the same town predicted by this technique. Since that time, a
number of more sophisticated techniques have been developed to determine the
ï¿½geographical profileï¿½ of a suspected serial criminal based on the locations of the crimes.
Your team has been asked by a local police agency to develop a method to aid in their
investigations of serial criminals. The approach that you develop should make use of at
least two different schemes to generate a geographical profile. You should develop a
technique to combine the results of the different schemes and generate a useful prediction
for law enforcement officers. The prediction should provide some kind of estimate or
guidance about possible locations of the next crime based on the time and locations of the
past crime scenes. If you make use of any other evidence in your estimate, you must
provide specific details about how you incorporate the extra information. Your method
should also provide some kind of estimate about how reliable the estimate will be in a
given situation, including appropriate warnings.
In addition to the required one-page summary, your report should include an additional
two-page executive summary. The executive summary should provide a broad overview
of the potential issues. It should provide an overview of your approach and describe
situations when it is an appropriate tool and situations in which it is not an appropriate
tool. The executive summary will be read by a chief of police and should include
technical details appropriate to the intended audience.
2010 ICM Problem
PROBLEM C: The Great Pacific Ocean Garbage Patch
Your ICM submission should consist of a 1 page Summary Sheet and a 10 page report/solution for a total of 11 pages.
To view and print problem C, you will need to have the Adobe Acrobat Reader installed in your Web browser. Downloading and installing Acrobat is simple, safe, and only takes a few minutes.
Download Acrobat Here
Click the Title Below To View a PDF of Problem C
The Great Pacific Ocean Garbage Patch