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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:

    130km/h
    50km/h
    120km/h
    need more info
    70km/h

    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

    Astronuc

    User Avatar

    Staff: Mentor

    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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