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Math Help - [SOLVED] velocity - component form

  1. #1
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    Post [SOLVED] velocity - component form

    Here is the problem:
    An airplane is flying on bearing of 194 at 460 mph. Find component form of velocity of airplane.

    Here is what I have done...is it correct?
    194 => 166
    v = (460cos166)i + (460sin166)j
    v = <460cos166, 460sin166>
    v = <-446.3, 111.29>

    Thanks!
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    Here is the problem:
    An airplane is flying on bearing of 194 at 460 mph. Find component form of velocity of airplane.

    Here is what I have done...is it correct?
    194 => 166
    v = (460cos166)i + (460sin166)j
    v = <460cos166, 460sin166>
    v = <-446.3, 111.29>

    Thanks!
    I assume that the x-axis of the coordinate system is pointing East and the y-axis is pointing North. If so

    \vec v = 460 \cdot (\cos(104^\circ\ ,\ \sin(104^\circ)
    Attached Thumbnails Attached Thumbnails [SOLVED] velocity - component form-kurs_komp.png  
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  3. #3
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    Shouldn't a bearing of 194 correspond to an angle of 256 (or -104) in standard position?


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  4. #4
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    Quote Originally Posted by yeongil View Post
    Shouldn't a bearing of 194 correspond to an angle of 256 (or -104) in standard position?


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    How do you know what angle 194 corresponds to?
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  5. #5
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    Quote Originally Posted by live_laugh_luv27 View Post
    How do you know what angle 194 corresponds to?
    The way I learned it in navigation 0 = North, 90 = East, 180 = South, and 270 = West. So 194 is 14 to the west of south. Now in the Cartesian plane, the terminal side would be in Quadrant III (look at earboth's diagram). The negative y-axis is now 270, so 14 to the west of this axis means you subtract 14 from 270, getting 256.


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  6. #6
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    so, would the answer be, <-111.28, -446.336>, or <111.28, 446.336>?
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  7. #7
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    Quote Originally Posted by live_laugh_luv27 View Post
    so, would the answer be, <-111.28, -446.336>, or <111.28, 446.336>?
    <-111.28, -446.336>. In standard representation the head of this vector would be in Quadrant III. The head of the other vector you list is in Quadrant I.


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  8. #8
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    Smile

    great, thanks!
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