Chapter3
ProjectileMotionNotes
Introduction
 NonlinearMotionMotionalongacurvedpath.
e.g.throwingabaseball,cannon,ballrolling
offtable.
 2independent“components”ofmotion:
Horizontal=remainsconstantw/oaforceactingonit.
Vertical=changesw/time,gpullsobject↓at10m/s/s.
→Combinedeffectsproduceacurvedpath,however,
neithercomponentaffectstheother.
 Vectors(arrows)helpusunderstandthismotion.
3.1VectorandScalarQuantities
 Vectorquantity:Aquantitythatrequiresboth
magnitude&direction.
e.g.velocity,acceleration
 Scalarquantity:Aquantitythatisdescribedby
magnitudeonly.Canbeadded,subtracted,multiplied
&divided.
e.g.mass,volume&time
 Arrowsareusedtorepresentvectorquantities.
lengthofarrow=magnitude
directionofarrow=directionofvectorquantity
3.2VelocityVectors
FollowontheBoard
 Supposeanairplaneisflyingnorthat100km/h
andthereisatailwindblowingnorthata
velocityof20km/h.
 Supposethesameairplaneturnsaroundand
fliesintothewind.
 Supposeanairplaneflyingnorthat80km/h
caughtastrongcrosswindof60km/hblowing
westtoeast.
3.2Continued…


Resultant:theresultofaddingtwovectors.
Howdoyoufindtheresultant?
Vectorsatrightangles:
1.
2.
3.
Draw2vectorswithtailstouching
Drawparallelprojectionofeachvectorwithdashedlines
Drawthediagonal(frompointwheretailsaretouching)
Vectorsnotatrightangles:
1.
Formaparallelogram,theresultantisitsdiagonal.
Note:Toadd2vectorsthatareequalinmagnitude&atright
angles,weuseasquare.Thediagonalisthesquarerootof
2or1.414timesthelengthofoneofitssides.
3.3ComponentsofVectors


Anyvectorcanbebrokendownintoit’svertical
andhorizontalvectors,calledcomponents.
Resolution:processofdeterminingthe
componentsofavector.(p.32,Figure3.7)
VerticalandHorizontallinesaredrawnfromthetail
ofthevector.
2. Arectangleisdrawnthatenclosesthevectorasits
diagonal.
3. Sidesoftherectanglearethedesiredcomponents.
1.
3.4ProjectileMotion
Projectiles:stonethrowninair,cannonball,etc.
 ProjectileMotion:
→Horizontalvelocity remains constantwhennohorizontalforce
actsonprojectile.
→Verticalvelocity changesduestogravity.
 Combinedaffectproducescurvedpath,parabola.

3.5UpwardlyLaunchedProjectiles
Nogravity=projectile
followsstraightlinepath.
 Withgravity=projectile
fallsbeneathline,same
verticaldistanceitwould
fallfromrest.
 d=gt2ord=5t2

3.5Continued…
 Figure3.11,p.36
•
•
•
Horizontalcomponentisalwaysthesame
Verticalcomponentchanges
Resultant=diagonalofrectangleformed
 Figure3.12,p.36
•
Initialvelocityisgreaterduetoincreaseinangle=higherpath
 Figure3.13,p.36
•
•
•
•
Pathsofprojectileswithsameinitialspeedbutdifferentprojectionangles.
Projectilesreachdifferentheight&horizontaldistances.
Distanceisthesameforprojectileslaunchedatanglesthataddupto90
degrees.
Maximumrangeordistanceisobtainedat45degreeangle
 Ifairresistanceissmall,itwilltakethesameamountoftimeforprojectile
toreachitsmaxheightasitdoestofall
 Forshortrangeprojectiles,assumegroundisflat.
Longrangeprojectiles,accountforearth’scurvature.
3.6FastMovingProjectilesSatellites
 EarthSatellite:aprojectile
travelingfastenoughtofall
aroundtheearthratherthan
intoit.
→Thisspeedis8km/sor
18,000mi/h
 Satellitesorbitaboveearth’s
atmosphereinordertoavoid
airdragandburningup.
→Can’tavoidgravity!