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Math Help - Vector Velocity

  1. #1
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    Vector Velocity

    Hi

    Can someone verify these answers are correct (or at least say where I went wrong)? Thanks

    v_{b} = velocity of bee in still air (speed = 6.7ms^-1; directon = N25 degrees E)
    v_{b} = 6.7cos(90-25)i + 6.7sin(90-25)j = 2.8315i + 6.0723j

    v_{w} = velocity of the wind (speed = 10.3ms^-1; direction = S54 degrees E)
    v_{w} = 10.3cos(90+54)i + 10.3sin(90+54)j = -8.3329i + 6.0542j

    v = resultant velocity of bee
    v_{b} + v_{w} = (2.8315i + -8.3329i) + (6.0723j + 6.0542j)
    v_{b} + v_{w} = v = -5.5013i + 12.1265j

    Convert v into geometric form and find the overall speed of the bee and it's direction of travel as a bearing:

    \abs{v} = sqrt((-5.5013)^2 + 12.1265^2) = sqrt(177.3155) = 13.3 ms^-1

    Angle = arctan(12.1265/-5.5013) = arctan(2.2043) = 1.1449 = 65.6 degrees

    Second quadrant = 180 - 65.5979 = 114.4 degrees

    bearing = N(114.4-90) degrees W = N24.4 degrees W

    Find the time taken by the bee to travel 1km:

    Time to travel 1km = 1000 / 13.3160 = 82.5 seconds

    Find the distance west it travels in that time

    Distance west = 82.4644 * -8.3329 = 687 metres
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by preid View Post
    Hi

    Can someone verify these answers are correct (or at least say where I went wrong)? Thanks

    v_{b} = velocity of bee in still air (speed = 6.7ms^-1; directon = N25 degrees E)
    v_{b} = 6.7cos(90-25)i + 6.7sin(90-25)j = 2.8315i + 6.0723j

    v_{w} = velocity of the wind (speed = 10.3ms^-1; direction = S54 degrees E)
    v_{w} = 10.3cos(90+54)i + 10.3sin(90+54)j = -8.3329i + 6.0542j
    Taking the x axis as E and the y axis as N

    [tex]v_{w}[/MATh] = velocity of the wind (speed = 10.3ms^-1; direction = S54 degrees E)
    v_{w} = 10.3\cos(-90+54)i + 10.3\sin(-90+54)j = +8.3329i - 6.0542j
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by preid View Post
    Hi

    Can someone verify these answers are correct (or at least say where I went wrong)? Thanks

    v_{b} = velocity of bee in still air (speed = 6.7ms^-1; directon = N25 degrees E)
    v_{b} = 6.7cos(90-25)i + 6.7sin(90-25)j = 2.8315i + 6.0723j

    v_{w} = velocity of the wind (speed = 10.3ms^-1; direction = S54 degrees E)
    v_{w} = 10.3cos(90+54)i + 10.3sin(90+54)j = -8.3329i + 6.0542j
    Taking the x axis as E and the y axis as N (and angles measured in degrees)

    [tex]v_{w}[/MATh] = velocity of the wind (speed = 10.3ms^-1; direction = S54 degrees E)

    v_{w} = 10.3\cos(-90+54)i + 10.3\sin(-90+54)j = +8.3329i - 6.0542j
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