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Math Help - vectors/displacement problem

  1. #1
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    vectors/displacement problem

    A jogger travels a route that has two parts. The first is a displacement A of 2.90 km due south, and the second involves a displacement B that points due east.
    (1) The resultant displacement A + B has a magnitude of 4.55 km. What is the magnitude of B?
    What is the direction of A + B relative to due south?

    (2) Suppose that A - B had a magnitude of 4.55 km. What then would be the magnitude of B and what is the direction of A - B relative to due south?
    direction of A - B relative to due south
    for part1:
    A^2+B^2+C^2 = 0

    B = \sqrt{A^2+(-C^2)}

    B = \sqrt{(2.9)^2+(-4.55)^2}

    B = 5.395 km

    some how that answer is wrong, can someone explain?
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  2. #2
    o_O
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    When you draw the vectors, you form a right triangle:

    Code:
        |\
        | \   
    2.9 |  \   4.55 
        |   \
        |    \
        V----->
            B
    By the Pythagorean theorem, 2.9^2 + B^2 = 4.55^2

    For part 2, A - B = A + (-B):

    Code:
             /|
            / |
     A - B /  |  A
          /   |
         /    |
        *<----V
           B
    The triangle doesn't change from part (1) and so the magnitudes should all be the same (but not the direction).

    You can see that the direction of A - B is south and to the west by a few degrees. Use trigonometry to find the upper angle to determine the exact direction.
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  3. #3
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    i did the Pythagorean theorem wrong. thanks!
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