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Vector (Relative velocity question)

  1. Nov 3, 2011 #1
    1. The problem statement, all variables and given/known data

    An observer, on a ship A sailing to the north with speed of 7km/h, saw a ship B. Ship B seems to be moving to south-east with a speed of 12√2 km/h.

    Find the direction which B is heading to.

    2. Relevant equations



    3. The attempt at a solution

    Let i and j be the unit vectors in the direction of eat north respectively and VA = velocity of ship A and VB = velocity of ship B.

    Now, VA = 7j

    BVA = 12i - 12j

    VB
    = BVA + VA
    =12i - 5j

    so θ = tan-15/12 = 22.6°

    The direction of ship B is E22.6°S.

    But the answer given is N67°23'E, which step is incorrect? Can anyone enlighten me?
     
  2. jcsd
  3. Nov 3, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Your answer looks fine to me. Are you sure the book's answer wasn't S67°23'E, which would be pretty close to yours.
     
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