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Math Help - Magnitude of displacement vector

  1. #1
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    Magnitude of displacement vector

    A jet-ski leaves the dock and travels 2km north. It then goes 1.4 km southeast and stops near a large boulder. What is the magnitude of the vector representing the jet ski's displacement from the dock to the boulder.

    I did the question and my answer was 1.414284887km however the answer booklet says 1.1km, im I doing something wrong?

    If yes plz guide me through this question.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    I would use the law of cosines for this one

    So the dude goes 2km north and then makes a 135 degree turn to the right and goes 1.4km

    we have everything we need.


    cos135=2^2+1.4^2-a^2)/2[(2)(1.4)]=(4+1.96-a^2)/5.6

    =5.96-a^2/5.6

    Can you finish up?
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  3. #3
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    well using the formula you gave i get 3.149571078, however the final answer is suppose to be 1.1km
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Try again, but this time let b=1.4 , c=2
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  5. #5
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    Quote Originally Posted by Solid8Snake View Post
    A jet-ski leaves the dock and travels 2km north. It then goes 1.4 km southeast and stops near a large boulder. What is the magnitude of the vector representing the jet ski's displacement from the dock to the boulder.

    I did the question and my answer was 1.414284887km however the answer booklet says 1.1km, im I doing something wrong?

    If yes plz guide me through this question.
    The angle from the dock to the point 2 km north to the boulder is 45 degrees.
    The length of the hypotenuse of a triangle with sides of length 1 is \sqrt 2 or approx 1.4

    The boulder point is 45 degrees east of north at a distance of about 1.4 km. or 1.010050506 km north and 0.989949494 km east of the dock.

    Your answer is correct.
    The booklet has a typo -- sometimes teachers will do that to see who is paying attention.
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  6. #6
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    thx guys, I greatly appreciate the help
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