233ModelinginCalculusIMickA.Sanzotta,DuffCampbellScenario1:CombinedArmsLiveFireWhileparticipatinginCadetFieldTraining(CFT)inthesummerof’99,youandyourcompanyaresenttoFt.Knoxtoconductmountedmaneuvertraining.YouareplacedinchargeoftheairstrikeportionoftheCombinedArmsLiveFireExercise(CALFEX),involvingAirForceA10sandArmyAttackHelicopters.YourmissionistoensuretheAirForceA10sandArmyAttackHelicoptersdelivertheirordnanceattheappropriatetimeandplace,andthattheairunitsmaintainaminimumsafeseparationdistanceof2nauticalmiles.At1400hours,theOICprovidesyouwiththefollowingsituation:•At1430hrsAirForceA10swillbe171nauticalmilesfromthetargetareaapproachingat206knotsonaheadingof303degrees.•At1430hrstheArmyAttackHelicoptersare88nauticalmilesfromthetargetarea,approachingat103knotsonaheadingof213degrees.TheOICwantstoknowhowfastthedistancebetweenthetwoairunitswillbechangingat1430hrsandiftheaircraftunitsmaintainaminimumsafedistancethroughoutthemission.Problem1:Determineareferencesystemtoexaminetheratesoftheaircraft.Solution1:ReferenceSystem:Positiveismovingawayfromthetarget.Thetargetistheorigin.Timezero(t=0)isnow(1430)hrs.Problem2:Definetheknownvariablesandconstants.Solution2:variables:c(t)isthedistancebetweenthe2airunitsattimet.(Hypotenuse)a(t)isthedistancethearmyhelicoptersarefromthetarget.a(t)=-103t+88b(t)isthedistancetheairforceA-10’sarefromthetargetattimet.b(t)=-206t+171t(0)is1430hrs.TARGETa(t)b(t)c(t)Figure1:SketchoftheAirMission234ArmyAttackHelicoptersAirForceA-10sa(0)=88nmb(0)=171nmanglA=303degreesangleB=213degreesa’(t)=103knotsb’(0)=206knotsProblem3:Statesomeassumptionsforthismodelingproblem.Solution3:1.Bothairunitswillmaintaintheirgivencourseandspeed.2.Bothairunitswillmaintainthesamealtitude.3.Theaircraftunitsmaintainatightformationandcanbeconsideredtobeonepointinspace.Problem4:Determinetheanglebetweenthe2aircraftunitsandtherelationshipbetweentheunits.Solution4:Theanglebetweenthe2aircraftunits,angle=|anglA–anglB|.Therefore,angle=90degrees.Therefore,PythagoreanTheoremapplie...
