2010_-2014mcm建模竞赛美赛题目中英文双语翻译版

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1、PROBLEMA:TheSweetSpotExplainthe"sweetspot"onabaseballbat.Everyhitterknowsthatthereisaspotonthefatpartofabaseballbatwheremaximumpoweristransferredtotheballwhenhit.Whyisn’tthisspotattheendofthebat?Asimpleexplanationbasedontorquemightseemtoidentifytheendofthebatasthesweetspot,butthisisknowntobeempirica

2、llyincorrect.Developamodelthathelpsexplainthisempiricalfinding.Someplayersbelievethat〃corking〃abat(hollowingoutacylinderintheheadofthebatandfillingitwithcorkorrubber,thenreplacingawoodcap)enhancesthe"sweetspot"effect.Augmentyourmodeltoconfirmordenythiseffect.DoesthisexplainwhyMajorLeagueBaseballproh

3、ibits"corking”？Doesthematerialoutofwhichthebatisconstructedmatter?Thatis,doesthismodelpredictdifferentbehaviorforwood(usuallyash)ormetal(usuallyaluminum)bats?IsthiswhyMajorLeagueBaseballprohibitsmetalbats?MCM2010A题：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景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

4、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？PROBLEMB:CriminologyIn1981PeterSutcliffewasconvictedofthirteenmurdersandsubjectinganumberofotherpeo

5、pletoviciousattacks.OneofthemethodsusedtonarrowthesearchforMr.Sutcliffewastofinda"centerofmass"ofthelocationsoftheattacks.Intheend,thesuspecthappenedtoliveinthesametownpredictedbythistechnique.Sincethattime,anumberofmoresophisticatedtechniqueshavebeendevelopedtodeterminethe"geographicalprofile"ofasu

6、spectedserialcriminalbasedonthelocationsofthecrimes.Yourteamhasbeenaskedbyalocalpoliceagencytodevelopamethodtoaidintheirinvestigationsofserialcriminals.Theapproachthatyoudevelopshouldmakeuseofatleasttwodifferentschemestogenerateageographicalprofile.Youshoulddevelopatechniquetocombinetheresultsofthed

7、ifferentschemesandgenerateausefulpredictionforlawenforcementofficers.Thepredictionshouldprovidesomekindofestimateorguidanceaboutpossiblelocationsofthenextcrimebasedonthetimeandlocationsofthepastcrimes