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Math Help - maximum velocity of a particle with 3d vector equation

  1. #1
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    maximum velocity of a particle with 3d vector equation

    Find the maximum speed of a particle whose velocity v m/s, at any time t seconds is given by v =2sin(t) i +  cos(t) j + 3 k.
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  2. #2
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    Quote Originally Posted by shawli View Post
    Find the maximum speed of a particle whose velocity v m/s, at any time t seconds is given by v =2sin(t) i + cos(t) j + 3 k.
    Dear shawli,

    v=2\sin{t}\underline{i}+\cos{t}\underline{j}+3\und  erline{k}

    Therefore,~speed~of~the~particle~(S)=\left|2\sin{t  }\underline{i}+\cos{t}\underline{j}+3\underline{k}  \right|

    S=\sqrt{(2sint)^2+cos^{2}t+9}

    S=\sqrt{3sin^{2}t+10}

    Since,~(sin^{2}t)_{max}=1

    S_{max}=\sqrt{13}\approx{3.61}

    Hope this will help you.
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  3. #3
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    <br />
\|\vec{v}\|^2=(2sin(t))^2+(cos(t))^2+9=3sin^2t+10\  leq 13 ~,~<br />
\|\vec{v}\|_{max}=\sqrt{13}<br />
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