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Math Help - [SOLVED] Finding the speed from the velocity

  1. #1
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    [SOLVED] Finding the speed from the velocity

    ok so the veloctiy is:

    v(t) = (-2sint)i + (3cost)j +4k

    so to find the speed you do

    squareroot((-2sint)^2 + (3cost)^2 +(4k)^2)
    =
    squareroot(4sin^2t + 9cos^2t + 16k^2)

    the book says the speed is 2 * squaroot(5)

    i have no idea how to get that from where i left it off.
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  2. #2
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    v(t) = -2\sin{t} \, \vec{i} + 3\cos{t} \, \vec{j}  + 4 \, \vec{k}

    |v| = \sqrt{4\sin^2{t} + 9\cos^2{t} + 16} = \sqrt{5\cos^2{t} + 20}

    the speed depends on t ... for what time, t = ? , did the problem want you to calculate the speed?
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  3. #3
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    Quote Originally Posted by skeeter View Post
    v(t) = -2\sin{t} \, \vec{i} + 3\cos{t} \, \vec{j} + 4 \, \vec{k}

    |v| = \sqrt{4\sin^2{t} + 9\cos^2{t} + 16} = \sqrt{5\cos^2{t} + 20}

    the speed depends on t ... for what time, t = ? , did the problem want you to calculate the speed?

    t = pie/2
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  4. #4
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    |v| = \sqrt{5\cos^2\left(\frac{\pi}{2}\right) + 20} = \sqrt{20} = 2\sqrt{5}
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