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Math Help - vectors at t<0

  1. #1
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    vectors at t<0

    I have the following information:

    A particle A of mass m is moving along a smooth horizontal surface with velocity of 2i + 3j. A second particle of mass 3m is moving with velocity 6i - 5j, collides with A at the origin at t=0. After this the particles coalesce.

    question:

    Find the expressions of Ra(t) and Rb(t), the respective position vectors of the particles A and B at time <0. Hence find the position vector of the centre of mass of the system before the collision. Hence determine the velocity of the centre of mass.

    how do i go about this?

    cheers
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  2. #2
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    Quote Originally Posted by thermalwarrior View Post
    I have the following information:

    A particle A of mass m is moving along a smooth horizontal surface with velocity of 2i + 3j. A second particle of mass 3m is moving with velocity 6i - 5j, collides with A at the origin at t=0. After this the particles coalesce.

    question:

    Find the expressions of Ra(t) and Rb(t), the respective position vectors of the particles A and B at time <0. Hence find the position vector of the centre of mass of the system before the collision. Hence determine the velocity of the centre of mass.

    how do i go about this?

    cheers
    This should get you started:

    Particle A: v_A = \frac{d r_A}{dt} = 2 i + 3 j \Rightarrow r_A(t) = (2t + C_1) i + (3t + C_2) j, ~ t \leq 0.

    But r_A(0) = 0 i + 0 j \Rightarrow C_1 = C_2 = 0.

    Therefore r_A(t) = (2t) i + (3t) j, ~ t \leq 0.
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  3. #3
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    Quote Originally Posted by thermalwarrior View Post
    I have the following information:

    A particle A of mass m is moving along a smooth horizontal surface with velocity of 2i + 3j. A second particle of mass 3m is moving with velocity 6i - 5j, collides with A at the origin at t=0. After this the particles coalesce.

    question:

    Find the expressions of Ra(t) and Rb(t), the respective position vectors of the particles A and B at time <0. Hence find the position vector of the centre of mass of the system before the collision. Hence determine the velocity of the centre of mass.

    how do i go about this?

    cheers
    This question links rather nicely with the one in this thread: http://www.mathhelpforum.com/math-he...-momentum.html
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  4. #4
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    so im correct in understanding from that reply the conditions at t=0 will hold for t<0?

    to find the centre of mass of the system could i assume that the two particles are joined some kind of rod to make the system whole or can i just use the equation for centre of mass:

    r = m1r1 + m2r2/m1+m2

    then differentiate the position vector to find the velocity???
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