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Determining Displacement Using Vector Components

  1. Aug 10, 2014 #1
    1. The problem statement, all variables and given/known data

    This problem has had me puzzled for hours. I really appreciate any help you can provide.

    A light plane leaves Shelburne, NS and flies 195km [N15°W] to Saint John, NB. After picking up a passenger, it flies to Moncton, NB which is 149km [N33°E]. The entire trip took 3.75h.

    Calculate the average velocity of the plane for the entire trip from Shelburne, NS to Moncton, NB.

    2. Relevant equations

    a2 + b2 = c2
    tan Θ = y-coordinates/x-coordinates

    3. The attempt at a solution

    dsjx = (-195) X cos75 = (-50.47)km W
    dsjy = 195 X sin75 = 188.36km N
    dmx = 149 X cos57 = 81.15km E
    dmy = 149 X sin57 = 124.96km N
    dx = (-50.47) + 81.15 = 30.68km E
    dy = 188.36 + 124.96 = 313.32km N

    r2 = 30.682 + 313.322
    r2 = 99110.68
    r = 314.8
    314.8/3.75 = 83.95/h

    tan θ = 313.32/30.68 = 10.21
    θ = 84.4

    The average velocity is 84km/h W 84 N.

    The books answer is 48km/h [W29°N]

    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 10, 2014 #2

    haruspex

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    I agree with your answer. I'd guess one of the given pieces of information has a wrongly stated compass direction, but I haven't been able to figure out exactly what. If these are real places, consult a map.
     
  4. Aug 10, 2014 #3
    Thank you. I did consult a map which says the distance between Shelburne NS and Moncton, NB is 262km which appears to be different than both mine and the books answers. I've double and triple checked the information provided and it's all accurate.

    I'm doing grade 11 physics via correspondence with nobody to ask questions to. Questions like these sort of ruin my flow. Do you think I should submit this answer?
     
  5. Aug 10, 2014 #4

    olivermsun

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    How do you interpret the heading W 84 N?
     
  6. Aug 10, 2014 #5

    haruspex

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    OK. The 33 degrees stated looks a bit low to me. Judging from Google maps it's more like 40 degrees, but that could be deceptive. Anyway, your answer is a lot closer to reality than the book answer. Submit it.
     
  7. Aug 12, 2014 #6

    Sorry for the delayed response

    84 degrees North of West
     
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