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Homework Help: Relative velocity ship problem intuitively

  1. Sep 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Two ships A and B are 4 km apart. A is due west of B. If A moves with uniform velocity of 8 km/hr due east and B moves with a uniform velocity of 6 km/hr due south. Calculate 1) the magnitudeof the velocity of A in relation to B 2) the closest distance apart of A and B

    2. Relevant equations
    The first solution is pretty simple but the second one, I dont get it. I know how to just solve it but without any intuition. Can someone help me get an intuitive idea of the solution of 2) ? The solution will be down there.

    3. The attempt at a solution
    In the example BD is drawn from B to relative velocity of A with respect to B represented by AE. From the given distance between A and B is 4km i.e. AB = 4km. In ABE sin x = BE/AE = 6/10 ( x= Angle EAB, BE = Velocity of B in opposite direction, AE = relative velocity of A in respect to B )
    Closest distance apart from A to B is BD.
    Now in BDA,
    BD = sin x * AB = sin 36.87 * 4 = 2.4 km
    This is the closest distance.

    Attached Files:

  2. jcsd
  3. Sep 24, 2016 #2


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    Posting tiny sideways pics is not a good way to get people to look at them.
  4. Sep 25, 2016 #3
    Dont have a good phone. Sorry. And vertical pictures are even tinier.
  5. Sep 25, 2016 #4


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    Gold Member

    The idea is to use B's reference frame. In that frame, what are the NS and EW components of A's motion. At what point does B perceive A as being at closest approach?
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