2010 MCM题目

 

A题：棒球棒上的最佳击球点

Explain the “sweet spot” 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 isn’t 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 “corking” 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 “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”?

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?

 

中文翻译：

解释棒球棒上的“最佳击球点”。

每一个棒球手都知道在棒球棒比较粗的部分有一个击球点，这里可以把打击球的力量最大程度地转移到球上。为什么这个点不在棒球棒的最末端？基于力矩的解释或许可以解释确定棒球棒的最末端就是最佳的击球点，但是实际当中并不是这样的。构建一个模型帮助解释实际当中的这个发现。

有一些棒球手相信在最佳击球点添充上软木塞可以提高打击效果（在球棒头部挖一个圆柱状槽，填充上软木塞或者橡皮）。进一步扩展模型确认或者否定该结论。这个解释是否可以解释为什么棒球联盟否定这种做法。

球棒是否和材质有关系，模型是否可以预测木头和金属球棒的不同打击效果？这是否是联盟禁止金属球棒的原因？

 

PROBLEM B: Criminology

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 “center of mass” 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 “geographical profile” 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.

 

中文翻译：

1981年Peter Sutcliffe(萨克利夫)被判刑因为他参与了十三起谋杀和对其他人的恶毒攻击。缩小搜索Sutcliffe的方法之一是发现一个攻击位置的“质心”.最终犯罪嫌疑人恰好生活在该方法预测的同一个小镇。从那时起，已经发展出一系列更加复杂的技术用来预测基于犯罪地点的具有地理效应（地理轮廓）的系列犯罪行为。

 

你的团队被一个当地警察局要求发展出一种方法用来帮助他们的系列犯罪调查。你们的方法应该至少需要利用两种不同的情景以生成地理效应（地理轮廓），进而根据不同情况下的分析结果对执法人员提供有效的预测。基于以往犯罪的时间和位置，预测信息应该提供一些估计或指导下次可能的犯罪地点。如果在预测中用到了其它的信息，必须提供特别的细节说明告诉我们这些信息是如何被整合的。你们的方法中也应该包括在给定条件下（包括适当警告信息）下预测的可靠性估计。

 

除了必要的一页小结，你们的报告应该包括两页额外的总结。这两页总结应该提供潜在问题的概述，它应该提供什么情况下，你们提出的方法是一个恰当的工具，在哪些情况下它不是。执行摘要将宣读了警察局长，并应包括适当的目标受众的技术细节。

 

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