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Relative Velocity - is the answer correct?

  1. Mar 4, 2015 #1
    1. The problem statement, all variables and given/known data
    An ant with a velocity of 20mm/s [W] crawls on a stick that is being dragged [W25 N] at 50mm/s. what is the velocity of the ant relative to the ground?

    2. Relevant equations
    Let A = ant, Let S=stick, Let G=ground, Let N and W be positive. Vag=?, Vas=20mm/s [W], Vsg=50mm/s[W25N]
    3. The attempt at a solution
    Vag=Vas + Vsg

    Vas = Vasx + Vasy
    = 20mm/s + 0mm/s

    Vsgx = Vsg(cos25)
    =50mm/s(cos25)
    =45.315 mm/s

    Vsgy= Vsg(sin25)
    =50mm/s(sin25)
    =21.130mm/s

    Vagx=Vasx +Vsgx
    =20mm/s+45.315mm/s
    =65.3mm/s

    Vagy= Vasy + Vsgy
    = 0mm/s +21.130mm/s
    =21.1mm/s

    V2ag=V2agx +V2agy
    Vag= (65.3mm/s)2+(21.1mm/s)2 - This is square root as well
    Vag=68.6mm/s

    Tan@= O/A
    @= Tan-1(21.1mm/s / 65.3mm/s)
    @= 17.9
    @=18

    Therefore the Ant s velocity relative to the ground is 68.6mm/s [W18N]
     
  2. jcsd
  3. Mar 4, 2015 #2

    BiGyElLoWhAt

    User Avatar
    Gold Member

    That's what I get as well.
     
  4. Mar 5, 2015 #3
    Thank you!
     
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