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Homework Help: Relative velocities

  1. Oct 8, 2007 #1
    1. The problem statement, all variables and given/known data

    A small plane flies at 120km/h over the end of a runway along the axis of the runway. There is a crosswind, exactly 90 degrees to the direction of the runway, blowing at 50km/h. The speed of the plane with respect to the air is:

    need more info

    2. Relevant equations

    3. The attempt at a solution

    I set up the equation:

    V(p/g) ( plane respect to ground ) = V(p/a) (plane respect to air) + V(a/g) (air respect to ground)

    p/g = 120 a/g =50

    120 = 50 +x
    sqrt(120^2 - 50^2) = x ?

    this gives 109 km/h though which is not a choice, did I do something wrong?
  2. jcsd
  3. Oct 8, 2007 #2


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    Staff Emeritus
    Science Advisor

    Why this?

    The plane is flying straight with the runway at 120 mph, and the plane has to be moving through the air. The wind is blowing cross-wise so the planes velocity in the air must be the vector sum of its velocity and the winds velocity.
  4. Oct 8, 2007 #3
    Why are you taking the square root? Everything is in the same direction.
  5. Oct 8, 2007 #4
    how is everything in the same direction if the wind is blowing perpindicular to the runway
  6. Oct 8, 2007 #5
    so it is 130?

    the reason i was subtracting was because I tried putting it into the equation

    V p/a = V p/b + V b/a

    and i got

    120 = x + 50
  7. Oct 8, 2007 #6
    Oh, I guess I don't know what crosswise means. I thought it meant across the cross section. Why not just say perpendicular, or if they really want to be fancy, orthogonal. I guess I am still an idiot for not even reading the 90 degree part, my bad. Yes, it would be 130.

    Do the vector diagram, and it should be pretty apparent.
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