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CONSTANT VELOCITY COMPONENTS I would suggest you take notes like this: Boat on River 10 m / s 5 m / s 11 m / s θ 50 m N S E W The boat travels East at 10 m / s . The river is 50m across. How long does it take the boat to cross the river? 5 seconds = 26.6 o 50 m 10 m / s = = 5 s v x t = d x v x v x t v x = d x t t v x = d x v x t =d x t x t v x = d x x t v = √ v x 2 +v y 2 v = √ (10 m / s ) 2 + (5 m / s ) 2 = 11 m / s dy =vyt = (5 m /s)(5 s) = 25 m ( ) 5 m /s 10 m /s θ = tan 1 (O/A) θ = tan 1 θ = 26.6 0 South of East The river flows South at 5 m / s . How long does it take the boat to cross the river? How fast does the boat travel? Here's the tough one: How far downstream does the boat land? At what angle (relative to East) is the boat swept downstream?

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  • CONSTANTVELOCITYCOMPONENTS

    Iwouldsuggestyoutakenoteslikethis:

    BoatonRiver

    10m/s

    5m/s11 m/s

    50m

    N

    S

    EW

    TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver?

    5seconds

    =26.6o

    50m10m/s= =5s

    vxt=dx

    vxvxt

    vx=dx

    t

    tvx=dx

    vxt=dx

    tx tvx=dxxt

    v= vx2+vy2

    v= (10m/s)2+(5m/s)2=11m/s

    dy=vyt=(5m/s)(5s)=25m

    ()5m/s10m/s=tan1(O/A)

    =tan1

    =26.60SouthofEast

    TheriverflowsSouthat5m/s.

    Howlongdoesittaketheboattocrosstheriver?

    Howfastdoestheboattravel?

    Here'sthetoughone:Howfardownstreamdoestheboatland?

    Atwhatangle(relativetoEast)istheboatsweptdownstream?

  • TheboattravelsEastat10m/s.Theriveris50macross.

    SMART Notebook

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver?

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver?

    10m/s

    50m

  • 50mvxt=dx

    10m/s= =5s

    TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver?

    10m/s

    50m

    tvx=dx

    vxt=dx

    tx tvx=dxxt

    vxvxt

    vx=dx

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    TheriverflowsSouthat5m/s.

    Howlongdoesittaketheboattocrosstheriver?

    10m/s

    50m

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    TheriverflowsSouthat5m/s.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    10m/s

    50m

    5m/s

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    TheriverflowsSouthat5m/s.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    Howfastdoestheboattravel?

    50m

    10m/s

    5m/s

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    TheriverflowsSouthat5m/s.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    Howfastdoestheboattravel?

    50m

    10m/s

    5m/s11 m/s v= vx2+vy2

    v= (10m/s)2+(5m/s)2=11m/s

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    TheriverflowsSouthat5m/s.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    Howfastdoestheboattravel?11m/s

    Here'sthetoughone:Howfardownstreamdoestheboatland?

    50m

    10m/s

    5m/s11 m/s

  • TheboattravelsEastat10m/s.Theriveris50macross.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    TheriverflowsSouthat5m/s.

    Howlongdoesittaketheboattocrosstheriver? 5seconds

    Howfastdoestheboattravel?11m/s

    Here'sthetoughone:Howfardownstreamdoestheboatland?

    50m

    10m/s

    5m/s11 m/s

    dy=vyt=(5m/s)(5s)=25m

  • Atwhatangle(relativetoEast)istheboatsweptdownstream?50m

    10m/s

    5m/s11 m/s

  • Atwhatangle(relativetoEast)istheboatsweptdownstream?50m

    10m/s

    5m/s11 m/s

    N

    S

    EW

  • Ohno......ItsThetaMonster!!!

    ='Theta'

    VECTORS ALWAYS HAVE DIRECTION!!!

  • TRIGIDENTITIES:

    PutthesenotesonaSEPARATEPAGE!!!

    SOHCAHTOA

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

    sin=O/H =sin1(O/H)cos=A/H =cos1(A/H)tan=O/A =tan1(O/A)

    OATAHCOHS

  • ToanswerthatweneedsomeSOHCAHTOA!!!

  • ToanswerthatweneedsomeSOHCAHTOA!!!

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

    sin=O/H

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

    sin=O/Hcos=A/H

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

    sin=O/Hcos=A/Htan=O/A

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

    sin=O/H =sin1(O/H)cos=A/Htan=O/A

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

    sin=O/H =sin1(O/H)cos=A/H =cos1(A/H)tan=O/A

  • ToanswerthatweneedsomeSOHCAHTOA!!!

    HO

    A

    H=HypotenuseO=OppositeA=Adjacent=theangle(indegrees)

    sin=O/H =sin1(O/H)cos=A/H =cos1(A/H)tan=O/A =tan1(O/A)

  • Findthe'MODE'buttononyourcalculator.MakesureyouaresettoDEGREES

    Thesin1,cos1andtan1arelocatedrightabovethe

    SIN,COSandTANbuttons.Hitthe

    2ndKeytoaccessthem.

  • Ilove...mmm...pie!

    ButweDON'TuseRADIANSinhere.

    WeDOuseDEGREE...

    becauseDEGREEsareHOT...

    ...orDEGREEsarecool...

    ...oratleastmeasuresofthat...

    ...butwho'scounting...

    DEGREEs?

  • OAT OATAHC AHCOHS OHS

    H O

    A

    H O

    A

  • Sobacktoourproblem...

  • Atwhatangle(relativetoEast)istheboatsweptdownstream?50m

    10m/s

    5m/s11 m/s

    N

    S

    EW

  • Atwhatangle(relativetoEast)istheboatsweptdownstream?

    Allofthesework:=sin1(O/H)=cos1(A/H)=tan1(O/A)

    50m

    10m/s

    5m/s11 m/s

    N

    S

    EW

  • Atwhatangle(relativetoEast)istheboatsweptdownstream?

    Allofthesework:=sin1(O/H)=cos1(A/H)=tan1(O/A)

    Let'susetan1:

    50m

    10m/s

    5m/s11 m/s

    N

    S

    EW

  • ()

    Atwhatangle(relativetoEast)istheboatsweptdownstream?

    Allofthesework:=sin1(O/H)=cos1(A/H)=tan1(O/A)

    Let'susetan1:

    50m

    10m/s

    5m/s11 m/s

    N

    S

    EW

    =tan1(O/A)

    =tan1

    =26.60SouthofEast

    5m/s10m/s

  • 'Theta'

    = 26.6o SOUTH OF EAST

    DIRECTION:

  • 50m

    10m/s

    5m/s11 m/s

    =26.6o

    N

    S

    EW

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