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Team#281Pageof16
AnEnergyModelfortheStuntPerson


Assumptions:

.Thetotalmass(combinedweight)ofthestuntperson(65kg)andthemotorcycle(135kg)is200kg.
.Themotorcycleandthestuntperson(MASP),areviewedideallyasarectangularsolid,1.8mlong,0.5mwideand1.1mhigh.
.Toguaranteesafety,theeffectof4gisthemaximumlimitthatisallowed.
.Theelephantisviewedideallyasarectangularsolid,6mlong,1mwideand4mhigh.
.Itisreportedthat,toavoidinjury,theverticalvelocityofMASPcan’tbelargerthan6m/swhilereachingtheground[4].

Notations
(thelettersinparenthesesaretheunitsofvariables):

dthewidthofabox
htheheightofabox.
hmaxthealtitudeofthetoppointofMASPjumpingovertheelephant..
lthelengthofabox.
Ltheperimeterofabox(m).
Pthemaximumcompressionstrengthofabox(N).
Pmthesurfacingstrengthofpaper(N/m).
VxthehorizontalvelocityofMASP.
VytheverticalvelocityofMASP.
VsthemaximumverticalvelocityofMASPreachingthegroundsafely(6m/sinourmodel).
Wwork.

TheTrackofMASP

TheIdealModel--IgnoringAirResistance

TheTrackisshownasFigure1:
Figure1.MNisaslopetoacceleratethevelocity

Tojumpovertheelephantsuccessfully,thealtitudeofpointAandBofthetrackmustbenosmallerthanh,thatis:
HA=HB=
whereistheanglebetweenthevelocityandground.Givenan,wecangettheminimumvelocityofv(vmin)andthedistancebetweenpointDandE,whichisLDE=.
TheAirResistanceModel
--Takingairresistanceintoaccount

TheairresistancehassignificanteffectonthemotionofMASPandcannotbeignoredinthismodelsincetheMASP’svelocityislarge.Basedontheaboveanalysisandconclusions,wecannowtaketheairresistanceintoconsiderationanddothesimilaranalysisconveniently.
ThetrackisshownasFigure2:

Figure2.MNisaslopetoacceleratethevelocity
Sincethegravityismuchlargerthantheverticalairresistance,weonlyfocusonthehorizontalone.Theairresistanceisthequadraticfunctionofvelocity,that’sF=kv2,wherecoefficientkisaconstant[5].Basedonthisconclusion,wegetthefollowingequations:


Forthesameprinciplerelatedbefore,thealtitudeofpointAandpointBmustsatisfy:
HA=HB=－

Wecanalsoget:
LDE=Forfurtheranalysis,pleaseseeAppendixA.

TheRese