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Math Help - Vectors question

  1. #1
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    Vectors question

    Two ships, A & B, leave port O simultaneously. Ship A travels due north at 16km/h and ship B travels due east at 13km/h.
    Find the magnitude & direction of AB after:
    (i) 1 hour (ii) 3 hours (iii) t hours.

    There are more parts to this question which I may post later. This is pretty simple but the answer in the book for all parts gives direction as 141 degrees.
    I got an answer of 39 degrees from A. Is this acceptable or must answer be given as 141? I understand that 180-39 = 141, but I don't understand even why 141 is an acceptable answer. I have drawn quadrants and everything and just don't understand where it comes from and why...?

    If anyone could answer it would be appreciated.
    Thanks.
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  2. #2
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    Lexington, MA (USA)
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    Hello, BenLaden!

    Two ships, A and B, leave port O simultaneously.
    Ship A travels due north at 16 km/h and ship B travels due east at 13km/h.

    \text{Find the magnitude and direction of }\overrightarrow{AB}\text{ after:}

    . . (i) 1 hour . . (ii) 3 hours . . (iii) t hours.

    The answer in the book gives the direction as 141.
    I got an answer of 39 from A.
    Is this acceptable or must answer be given as 141 ?

    After one hour, we have this diagram:
    Code:
        A *
          |\
          | \
          |θ \
       16 |   \
          |    \
          |     \
          |      \
        O * - - - * B
             13

    You are correct . . . \theta = 39^o

    But information is useless unless it is clear where the angle is located.


    There are several methods for indicating the direction.
    Here are a few of them.

    [1] Bearing: measured clockwise from due North.
    . . .The bearing is: . 180^o - 39^o \:=\:141^o

    [2] Standard angle: measured CCW from due East.
    . . .The standard angle is: . -51^o

    [3] Heading: measured East or West of due North or due South.
    . . .The heading is: . S\:39^o\,E


    The problem should have stated the method of indicating the direction.

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