1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook