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Math Help - Finding an angle

  1. #1
    missashley
    Guest

    Finding an angle

    A ship cruises forward at Vs=5 m/s relative to the water. On deck, a man walks diagonally toward the bow such that his path forms an angle theta = 22 degrees with a line perpendicular to the boat's direction of motion. He walks at Vm = 2 m/s relative to the boat



    The speed he walks relative to the water is 5.749 m/s.

    At what angle to his intended path does the man walk with respect to the water? Answer in degrees.


    I was thinking maybe of using Tan-1(opposite/adjacent)
    or some thing to that effect

    It isn't 22 or 68 degrees
    Last edited by missashley; October 10th 2007 at 02:42 PM. Reason: More information
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  2. #2
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    Hello, missashley!

    A ship cruises forward at V_s = 5 m/s relative to the water.
    On deck, a man walks diagonally toward the bow such that his path forms
    an angle \theta = 22^o with a line perpendicular to the boat's direction of motion.
    He walks at V_m = 2 m/s relative to the boat.

    The speed he walks relative to the water is 5.749 m/s.

    At what angle to his intended path does the man walk with respect to the water?
    Answer in degrees.
    Code:
          B        C
          * - - → *
          ↑      /
          |     /
          |    / 2
          |22*/
          |  /
          | /
          |/
          *
          A

    In the right triangle, we have: . \begin{array}{ccccc}AB & = & 2\cos22^o & \approx & 1.854 \\<br /> <br />
BC & = & 2\sin22^o & \approx & 0.749\end{array}

    Relative to the ship, he is walking 0.749 m/sec forward.

    Since the ship is moving forward at 5 m/sec,
    . . the man is moving forward at 5.749 m/sec (relative to the water).
    (That's where they got that number.)

    So relative to the water, his movement looks like this:
    Code:
              5.749
          * - - - - - *
          |         /
          |       /
    1.854 |     /
          |   /
          |θ/
          *

    We have: . \tan\theta \:=\:\frac{5.749}{1.854} \:=\:3.100862999

    Hence: . \theta\:=\:\tan^{-1}(3.100863) \:\approx\:72.1^o

    Relative to the forward direction of the boat, his angle is about 17.9.

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