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Math Help - Mechanics Problem - Vectors

  1. #1
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    Mechanics Problem - Vectors

    A particle has position vector 2i + j initially and is moving with speed 10m/s in the direction 3i - 4j. Find its position vector when t = 3 and the distance it has travelled in those 3 seconds.

    My solution:
    Position vector = initial position + displacement
    since displacement = velocity x time
    then position vector= (2i + j) + 3(3i - 4j)
    = 2i + j + 9i - 12i
    = 11i - 11j
    and distance is straightforward, distance = speed x time so 10 x 3 which is 30m.
    My solution is however wrong, becuase in the question it says (3i - 4j) is the direction the particle is travelling in, not the velocity, so im kinda stuck and the right answer should be 20i - 23j according to the back of the book.

    How do i do this question? Also, if u find the velocity vector, and work out the magnitude, you should get the speed right? So if initial velocity is (2i + 3j) then the magnitude of this vector should equal the speed which is 10 m/s but it does not, the magnitude of this vector is the sqrt (2^2 + 3^2) which is root 13 and not 10 m/s so how does that work? Thanks for you help.
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  2. #2
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    Quote Originally Posted by MingMing View Post
    A particle has position vector 2i + j initially and is moving with speed 10m/s in the direction 3i - 4j. Find its position vector when t = 3 and the distance it has travelled in those 3 seconds.

    My solution:
    Position vector = initial position + displacement
    since displacement = velocity x time
    then position vector= (2i + j) + 3(3i - 4j)
    = 2i + j + 9i - 12i
    = 11i - 11j
    and distance is straightforward, distance = speed x time so 10 x 3 which is 30m.
    My solution is however wrong, becuase in the question it says (3i - 4j) is the direction the particle is travelling in, not the velocity, so im kinda stuck and the right answer should be 20i - 23j according to the back of the book.

    How do i do this question? Also, if u find the velocity vector, and work out the magnitude, you should get the speed right? So if initial velocity is (2i + 3j) then the magnitude of this vector should equal the speed which is 10 m/s but it does not, the magnitude of this vector is the sqrt (2^2 + 3^2) which is root 13 and not 10 m/s so how does that work? Thanks for you help.
    \displaystyle \vec{s} = \vec{s_0} + \vec{v}t

    Note that 3i - 4j is a vector in the direction of the velocity. It is not the velocity. The velocity will be the unit vector in the direction of 3i - 4j times the speed. Thus
    \displaystyle \vec{v} = \left ( \frac{3i - 4j}{|3i - 4j|} \right ) \cdot 10~\text{m/s}

    -Dan
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  3. #3
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    Thank you.
    Last edited by MingMing; March 6th 2011 at 10:04 AM.
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