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Plane ride relative motion problem

  1. Feb 11, 2016 #1
    1. The problem statement, all variables and given/known data
    You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 41 m/s at an angle of 30° west of due north.

    1) What is the speed of the plane with respect to the ground?

    2. Relevant equations
    VAB=VAC+VBC
    Pythagorean theorem
    Trigonometry
    (Not so sure about these)

    3. The attempt at a solution
    I know that VPG=VPA+VAG, but I'm not sure about how to break velocities into their components.
    I kept VPA at 160 since it only moves in one dimension (only east), and I tried breaking up VAG as such:

    41cos60i+41sin60j

    (60 degrees since that is the angle formed when putting VAG tip to tail with VPA)

    Added to VPA:
    236.507 m/s

    In searching various forums (this seems a common hw question), I've seen very different solutions than mine, so I know mine is wrong.

    Thanks a lot
     
    Last edited: Feb 11, 2016
  2. jcsd
  3. Feb 11, 2016 #2
    OK so I tried using the complementary angle of 120, and then added the i (160 + 41cos120) and j (41sin60) components, then put each into the Pythagorean theorem

    VPG=√(i-components2 + j-components2) = 143.9479, which is the right answer

    I'm unsure as to why 120 was the right angle to use... o_O
     
    Last edited: Feb 11, 2016
  4. Feb 11, 2016 #3

    SteamKing

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    Staff Emeritus
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    Homework Helper

    Always make a sketch. These are quite useful in showing how to decompose vectors into their components.

    Remember,to decompose a vector into its unit vector components in i and j, due east represents a heading angle of 0 degrees.
     
  5. Feb 13, 2016 #4
    Thanks, the confusion turned out to be coming from a bad drawing.
     
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