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Homework Help: Vectors componenets relative motion help

  1. May 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Hello. I was wondering if you guys could help me tell me why i am getting this problem wrong.

    Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 12.1 m/s due north. Plane 2 taxies with a speed of 6.3 m/s in a direction 21.2° north of west.
    (a) What are the direction and magnitude of the velocity of plane 1 relative to plane 2?
    Direction _______° north of east
    Magnitude ________m/s

    (b) What are the direction and magnitude of the velocity of plane 2 relative to plane 1?
    Direction ______° south of west
    Magnitude ________ m/s

    2. Relevant equations




    3. The attempt at a solution

    I First drew out a parallelogram with the magnitude and direction of plane 1 then drew plane 2's tail to the head of plane 1 to visualize the problem. Next i used components of a vector to solve for the magnitude and direction.

    plane 1 -> x = 12.1 cos 90 =0
    plane 2 -> x = 6.3 cos 21.2 = 5.874

    plane 1 -> y = 12.1 sin 90 = 12.1
    plane 2 -> y = 6.3 sin 21.2 = 2.278

    I added the vectors (5.874 m/s) x + (14.38 m/s) y

    To find the magnitude of the resultant i got sq root (5.874 m/s)^2 + (14.38 m/s)^2 = 15.53

    theta = inverse tan (14.378/5.8736) = 67.78 degrees

    b) I was confused on this one. I thought that from plane 2 the angle would be 67.78 + 180 = 247.8 degrees with the same magnitude of 15.53?

    I would greatly appreciate if someone could help me out and let me know what i did wrong. Thanks so much! :)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 12, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi P944! :smile:
    No, that will add the velocities.

    For a relative velocity, you always need to subtract.

    If g is "ground", then you want V12, which = V1g + Vg2 = V1g - V2g :wink:

    (if you draw arrows, this should be obvious)
     
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