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Homework Help: 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
    Pythagorean theorem
    (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:


    (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


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    Staff Emeritus
    Science Advisor
    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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