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Math Help - Vector help

  1. #1
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    Vector help

    Hey guys I need some help on this question...

    A spelunker is surveying a cave. She follows a passage 180m straight west, then 230m in a direction 45 degrees east of south, and then 280m at 30 degrees east of north. After a fourth unmeasured displacement, she finds herself back where she started.

    1. Use a scale drawing to determine the magnitude of the fourth displacement. 2. Determine the direction of the fourth displacement. Two sig digs.

    So where should I start I'm terrible at vectors.
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  2. #2
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    Re: Vector help

    Quote Originally Posted by Oldspice1212 View Post
    Hey guys I need some help on this question...

    A spelunker is surveying a cave. She follows a passage 180m straight west, then 230m in a direction 45 degrees east of south, and then 280m at 30 degrees east of north. After a fourth unmeasured displacement, she finds herself back where she started.

    1. Use a scale drawing to determine the magnitude of the fourth displacement. 2. Determine the direction of the fourth displacement. Two sig digs.

    So where should I start I'm terrible at vectors.
    acquire some graph paper and a protractor for the scale drawing ... sounds to me like this is a exercise in actual physical measuring using scale to come up with a solution.
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  3. #3
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    Re: Vector help

    Hello, Oldspice1212!

    I hope you're familiar with the basics of vectors.


    A spelunker is surveying a cave.
    She follows a passage 180m straight west,
    then 230m in a direction 45 degrees east of south,
    and then 280m at 30 degrees east of north.
    After a fourth unmeasured displacement, she finds herself back where she started.

    1. Use a scale drawing to determine the magnitude of the fourth displacement.
    What a clumsy way to get a measurement!

    2. Determine the direction of the fourth displacement. (Two sig. digits)

    Let North and East be positive.

    Going from A to B: 180 m west.
    . . \overrightarrow{AB} \;=\; \langle 180\cos180^o,\:180\sin180^o\rangle \;=\;\langle \text{-}180,\:0\rangle

    Going from B to C: 230 m, 45o east of south.
    . . \overrightarrow{BC} \;=\;\langle 230\cos(\text{-}45^o),\:230\sin(\text{-}45^o)\rangle \;=\; \langle 115\sqrt{2},\:\text{-}115\sqrt{2}\rangle

    Going from C to D: 280 m, 30o east of north.
    . . \overrightarrow{CD} \;=\;\langle 280\sin30^o,\:280\cos30^o\rangle \;=\; \langle 140,\:140\sqrt{3}\rangle

    Add the vectors:
    . . \overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CD} \;=\;\langle 115\sqrt{2} - 40,\:140\sqrt{3}-115\sqrt{2}\rangle \;\approx\;\langle 122.63,\:79.85\rangle

    Point D is 122.63 m east and 79.85 m north of point A.

    Code:
                            * D
                         *  *
                      *   θ *
                   *        * 79.85
                *           *
             *              *
        A *  *  *  *  *  *  *
                122.63
    \tan\theta \:=\:\frac{122.63}{79.85} \:=\:1.53575454

    . . . \theta \:=\:59.93000891^o

    The direction of the last displacement is: 60o west of south.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    By the way, the final magnitude is:

    . . . \sqrt{122.63^2 + 79.85^2} \;\approx\;146.3\text{ m.}
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  4. #4
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    Re: Vector help

    Thanks a ton so it would be 33 degrees south of west :P
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