2010 MCM棰樼洰
A棰橈細妫掔悆妫掍笂鐨勬渶浣冲嚮鐞冪偣
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?
涓枃缈昏瘧锛?/font>
瑙ｉ噴妫掔悆妫掍笂鐨?ldquo;鏈€浣冲嚮鐞冪偣”銆?/font>
姣忎竴涓鐞冩墜閮界煡閬撳湪妫掔悆妫掓瘮杈冪矖鐨勯儴鍒嗘湁涓€涓嚮鐞冪偣锛岃繖閲屽彲浠ユ妸鎵撳嚮鐞冪殑鍔涢噺鏈€澶х▼搴﹀湴杞Щ鍒扮悆涓娿€備负浠€涔堣繖涓偣涓嶅湪妫掔悆妫掔殑鏈€鏈锛熷熀浜庡姏鐭╃殑瑙ｉ噴鎴栬鍙互瑙ｉ噴纭畾妫掔悆妫掔殑鏈€鏈灏辨槸鏈€浣崇殑鍑荤悆鐐癸紝浣嗘槸瀹為檯褰撲腑骞朵笉鏄繖鏍风殑銆?span style="BACKGROUND: yellow; mso-highlight: yellow">鏋勫缓涓€涓ā鍨嬪府鍔╄В閲婂疄闄呭綋涓殑杩欎釜鍙戠幇銆?/span>
鏈変竴浜涙鐞冩墜鐩镐俊鍦ㄦ渶浣冲嚮鐞冪偣娣诲厖涓婅蒋鏈ㄥ鍙互鎻愰珮鎵撳嚮鏁堟灉锛堝湪鐞冩澶撮儴鎸栦竴涓渾鏌辩姸妲斤紝濉厖涓婅蒋鏈ㄥ鎴栬€呮鐨級銆?span style="BACKGROUND: yellow; mso-highlight: yellow">杩涗竴姝ユ墿灞曟ā鍨嬬‘璁ゆ垨鑰呭惁瀹氳缁撹銆傝繖涓В閲婃槸鍚﹀彲浠ヨВ閲婁负浠€涔堟鐞冭仈鐩熷惁瀹氳繖绉嶅仛娉曘€?/span>
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.
涓枃缈昏瘧锛?/font>
1981骞?/span>Peter Sutcliffe(钀ㄥ厠鍒╁か)琚垽鍒戝洜涓轰粬鍙備笌浜嗗崄涓夎捣璋嬫潃鍜屽鍏朵粬浜虹殑鎭舵瘨鏀诲嚮銆傜缉灏忔悳绱?/span>Sutcliffe鐨勬柟娉曚箣涓€鏄彂鐜颁竴涓敾鍑讳綅缃殑“璐ㄥ績”.鏈€缁堢姱缃珜鐤戜汉鎭板ソ鐢熸椿鍦ㄨ鏂规硶棰勬祴鐨勫悓涓€涓皬闀囥€備粠閭ｆ椂璧凤紝宸茬粡鍙戝睍鍑轰竴绯诲垪鏇村姞澶嶆潅鐨勬妧鏈敤鏉ラ娴嬪熀浜庣姱缃湴鐐圭殑鍏锋湁鍦扮悊鏁堝簲锛堝湴鐞嗚疆寤擄級鐨勭郴鍒楃姱缃涓恒€?/span>
浣犵殑鍥㈤槦琚竴涓綋鍦拌瀵熷眬瑕佹眰鍙戝睍鍑轰竴绉嶆柟娉曠敤鏉ュ府鍔╀粬浠殑绯诲垪鐘姜璋冩煡銆備綘浠殑鏂规硶搴旇鑷冲皯鑳藉鍦ㄤ袱绉嶄笉鍚岀殑鐜涓嬩骇鐢熷湴鐞嗘晥搴旓紙鍦扮悊杞粨锛夛紝杩涜€屾牴鎹笉鍚屾儏鍐典笅鐨勫垎鏋愮粨鏋滃鎵ф硶浜哄憳鎻愪緵鏈夋晥鐨勯娴嬨€傚熀浜庝互寰€鐘姜鐨勬椂闂村拰浣嶇疆锛岄娴嬩俊鎭簲璇ユ彁渚涗竴浜涗及璁℃垨鎸囧涓嬫鍙兘鐨勭姱缃湴鐐广€傚鏋滃湪棰勬祴涓敤鍒颁簡鍏跺畠鐨勪俊鎭紝蹇呴』鎻愪緵鐗瑰埆鐨勭粏鑺傝鏄庡憡璇夋垜浠繖浜涗俊鎭槸濡備綍琚暣鍚堢殑銆備綘浠殑鏂规硶涓篃搴旇鍖呮嫭鍦ㄧ粰瀹氭潯浠朵笅锛堝寘鎷€傚綋璀﹀憡淇℃伅锛変笅棰勬祴鐨勫彲闈犳€т及璁°€?/font>
闄や簡蹇呰鐨勪竴椤靛皬缁擄紝浣犱滑鐨勬姤鍛婂簲璇ュ寘鎷袱椤甸澶栫殑鎬荤粨銆?/span>杩欎袱椤垫€荤粨搴旇鎻愪緵娼滃湪闂鐨勬杩帮紝瀹冨簲璇ユ彁渚涗粈涔堟儏鍐典笅锛屼綘浠彁鍑虹殑鏂规硶鏄竴涓伆褰撶殑宸ュ叿锛屽湪鍝簺鎯呭喌涓嬪畠涓嶆槸銆傛墽琛屾憳瑕佸皢瀹ｈ浜嗚瀵熷眬闀匡紝骞跺簲鍖呮嫭閫傚綋鐨勭洰鏍囧彈浼楃殑鎶€鏈粏鑺傘€?/font>
|
