Lab 7: Projectile Motion
Lab 7: Projectile Motion
Lab 7: Projectile Motion
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<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Figure4:Whenaprojectile(water,inthiscase)islaunchedupward,theverticalaccelerationwillreachzeroatthetopoftheparabola.AsgravitypullstheobjecttowardtheEarth,theobjectaccelerates.Horizontalvelocityremainsconstantthroughoutthismotion.Figure5:Fourusefulkinematicequationsforprojectilemotion:Oneconvenientthingaboutusingvectorstodescribeprojectilemotionisthatwecanseparatethevelocityoftheprojectileintohorizontalandverticalmotion.Theverticalcomponentofthevelocitychangeswithtimeduetogravity,butthehorizontalcomponentremainsconstantbecausenohorizontalforceisactingontheobject(airresistanceaddsquiteabitofcomplicationathighervelocitiesbutwillbeneglectedinthislab).Sinceprojectilesmoveintwodimensions(verticalandhorizontal),thisallowsforindependentanalysisofeachcomponentoftheobject’smotion.Thecombinationofa(constantly)changingverticalvelocityandaconstanthorizontalvelocitygivesaprojectile’strajectorytheshapeofaparabola.AsshowninFigure3,theprojectilewithhorizontalandverticalmotionassumesacharacteristicparabolictrajectoryduetotheeffectsofgravityontheverticalcomponentofmotion.ThehorizontalmotionistheresultofNewton’sFirstLawinaction–theobject’sinertia!Ifairresistanceisneglected,therearenohorizontalforcesactinguponprojectile,andthusnohorizontalacceleration.Itmightseemsurprising,butaprojectilemovesatthesamehorizontalspeednomatterhowlongitfalls!Thekinematicsfromthepreviouslabcandescribebothcomponentsofthevelocityseparately.Formosttwodimensionalprojectilemotionproblems,thefollowingfourequationswillallowyoutosolvefordifferentaspectsofaprojectile’sflight,aslongasyouknowtheinitialpositionandtheinitialvelocity.Thetwonewequationscanbeobtainedthroughsubstitution.Inthislabyoucanassumethatprojectilesarefiredeitherverticallyorhorizontally,sothattheinitialvelocitiesineithercasewillbeeither:v o =v yo orv o =v xo. Usingtheequationsabove,youcancalculatethetotaldistanceorrange,R,ofaprojectile.Iftheprojectileisfiredatanangle,therangeisafunctionoftheinitialangle,theinitialvelocityandtheforceofgravity.Usingalittlealgebra,youcanderivethisexpressionusingthekinematicsequationsabove:81
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