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Math Help - Vectors

  1. #1
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    Vectors

    A particle P moves such that its position vector r with respect to the origin O at the time t is given by

    r = cos3ti + sin3tj

    a) Find an expression for v, the velocity of P at time t.

    b) Show that the direction of v is perpendicular to that of r for all values of t.

    c) Find the speed of P.

    OK for part a I'm assuming you differentiate r which i get

    v = -3sin3ti + 3cos3tj

    is this correct??Part b Im stumped with, not sure I've learned that.

    For part c i think maybe i use equation v=u+at ??
    if so how could i find t ?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by djmccabie View Post
    A particle P moves such that its position vector r with respect to the origin O at the time t is given by

    r = cos3ti + sin3tj

    a) Find an expression for v, the velocity of P at time t.

    b) Show that the direction of v is perpendicular to that of r for all values of t.

    c) Find the speed of P.

    OK for part a I'm assuming you differentiate r which i get

    v = -3sin3ti + 3cos3tj

    is this correct??Part b Im stumped with, not sure I've learned that.

    For part c i think maybe i use equation v=u+at ??
    if so how could i find t ?
    For part b) we know that if two vectors are perpendicular that the dot product is zero... so

    \vec r \cdot \vec v=(\cos(3t)(-3\sin(3t))+(\sin(3t)(3\cos(3t)=0

    Speed is the magnitutde of velocity so...

    \sqrt{\vec v \cdot \vec v}=...
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  3. #3
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    thanks pal. Did i do part a correctly?
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  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    yes
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