2010Co
testProblemsMCMPROBLEMS
PROBLEMATheSweetSpot
Explai
the“sweetspot”o
abaseballbatEveryhitterk
owsthatthereisaspoto
thefatpartofabaseballbatwheremaximumpoweristra
sferredtotheballwhe
hitWhyis
’tthisspotatthee
dofthebatAsimpleexpla
atio
basedo
torquemightseemtoide
tifythee
dofthebatasthesweetspotbutthisisk
ow
tobeempiricallyi
correctDevelopamodelthathelpsexplai
thisempiricalfi
di
gSomeplayersbelievethat“corki
g”abathollowi
goutacyli
deri
theheadofthebata
dfilli
gitwithcorkorrubberthe
replaci
gawoodcape
ha
cesthe“sweetspot”effectAugme
tyourmodeltoco
firmorde
ythiseffectDoesthisexplai
whyMajorLeagueBaseballprohibits“corki
g”Doesthematerialoutofwhichthebatisco
structedmatterThatisdoesthismodelpredictdiffere
tbehaviorforwoodusuallyashormetalusuallyalumi
umbatsIsthiswhyMajorLeagueBaseballprohibitsmetalbats
PROBLEMBCrimi
ology
I
1981PeterSutcliffewasco
victedofthirtee
murdersa
dsubjecti
ga
umberofotherpeopletoviciousattacksO
eofthemethodsusedto
arrowthesearchforMrSutcliffewastofi
da“ce
terofmass”ofthelocatio
softheattacksI
thee
dthesuspecthappe
edtolivei
thesametow
predictedbythistech
iqueSi
cethattimea
umberofmoresophisticatedtech
iqueshavebee
developedtodetermi
ethe“geographicalprofile”ofasuspectedserialcrimi
albasedo
thelocatio
softhecrimesYourteamhasbee
askedbyalocalpoliceage
cytodevelopamethodtoaidi
theiri
vestigatio
sofserialcrimi
alsTheapproachthatyoudevelopshouldmakeuseofatleasttwodiffere
tschemestoge
erateageographicalprofileYoushoulddevelopatech
iquetocombi
etheresultsofthediffere
tschemesa
dge
erateausefulpredictio
forlawe
forceme
tofficersThepredictio
shouldprovidesomeki
dofestimateorguida
ceaboutpossiblelocatio
softhe
extcrimebasedo
thetimea
dlocatio
softhepastcrimesce
esIfyoumakeuseofa
yotherevide
cei
yourestimateyoumustprovidespecificdetailsabouthowyoui
corporatetheextrai
formatio
Yourmethod
fshouldalsoprovidesomeki
dofestimateabouthowreliabletheestimatewillbei
agive
situatio
i
cludi
gappropriatewar
i
gsI
additio
totherequiredo
epagesummaryyourreportshouldi
cludea
additio
altwopageexecutivesummaryTheexecutivesummaryshouldprovideabroadoverviewofthepote
tialissuesItshouldprovidea
overviewofyourapproacha
ddescribesituatio
swhe
itisa
appropriatetoola
dsituatio
si
whichitis
ota
appropriatetoolTheexecutivesummarywillbereadbyachiefofpolicea
dshouldi
cludetech
icaldetailsappropriatetothei
te
dedaudie
ce
翻译（翻译来源：数学中国）问题A：最佳击球点
解释一下棒球棒的“最r