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Vectors: air speed, ground speed

  1. Oct 16, 2007 #1
    [SOLVED] Vectors: air speed, ground speed

    I'm having trouble drawing the diagram for this question.

    1. The problem statement, all variables and given/known data
    An airplane with air speed 120 km/h is heading due north in a wind blowing due east at 50 km/h. What is the ground speed of the plane?

    2. Relevant equations
    Pythagoras theorem.


    3. The attempt at a solution
    I've attached my version of the diagram with this message. I used the Pythagoras theorem since the wind blowing due east and the plane headed north meet at 90 degrees.

    ground speed = sq. root {(120^2 + 50^2)}
    = 130 km/h

    The answer is supposed to be 60 km/h. Can someone please help or tell me where I went wrong? Thank you!
     

    Attached Files:

    Last edited: Oct 16, 2007
  2. jcsd
  3. Oct 16, 2007 #2

    Astronuc

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    Staff: Mentor

    That is correct. The vectors are additive and the Pythagorean theorem applies since the wind is blowing due E of the plane traveling N.

    If the plane was just taveling due north with a wind speed of 120 km/h in still air, its ground speed would be 120 km/h. Only if there was a head wind of 60 km/h would it's ground speed by 60 km/h.

    Where did one find that the answer would be 60 km/h?
     
  4. Oct 16, 2007 #3
  5. Oct 17, 2007 #4

    Astronuc

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    Staff: Mentor

    The website indicates the incorrect answer.

    The air speed is due north at 120 km/h, the wind blow perpendicular (due E) at 50 km/h. Adding the vectors, gives a resultant 130 km/h, with respect to the ground.
     
  6. Oct 17, 2007 #5
    I was thinking that, but I needed to be sure since the site didn't offer an explanation. Again, thank you! :smile:
     
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