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Math Help - particle/curvature question

  1. #1
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    particle/curvature question

    Hi guys can anyone help me out with this?

    A moving particle at time t ∈ [0, 10] (seconds) has position vector in metres from the origin (0, 0, 0) given by the vector function r(t) = (10 − t)i + (t^2
    − 10t)j + sin tk.
    i. Describe the path of the particle, as seen from above (the positive k-direction), and also describe it in three dimensions.
    ii. Find the curvature of the path, at t = 2π ≈ 6.28 seconds.
    iii. Find the angle between the path (at start and end-points) and the k-direction.

    Thanks
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  2. #2
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    Quote Originally Posted by katie View Post
    Hi guys can anyone help me out with this?

    A moving particle at time t ∈ [0, 10] (seconds) has position vector in metres from the origin (0, 0, 0) given by the vector function r(t) = (10 − t)i + (t^2
    − 10t)j + sin tk.
    i. Describe the path of the particle, as seen from above (the positive k-direction), and also describe it in three dimensions.

    Mr F says:

    x = 10 - t => t = 10 - x .... (1)

    y = t^2 - 10t .... (2)

    Substitute (1) into (2).

    ii. Find the curvature of the path, at t = 2π ≈ 6.28 seconds.

    Mr F says: Substitute into the formula.

    iii. Find the angle between the path (at start and end-points) and the k-direction.

    Mr F says: Use the dot product.

    Thanks
    ..
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  3. #3
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    when you say substitute into the formula is that just into the r(t) formula?

    and the dot product, i am not sure what the other vector is to be using the dot product with?

    thanks
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  4. #4
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    Quote Originally Posted by jimmy View Post
    when you say substitute into the formula is that just into the r(t) formula?

    and the dot product, i am not sure what the other vector is to be using the dot product with?

    thanks
    The curvature formula.

    Direction of motion given by dr/dt. Evaluate at t = 0 and t = 10. Consider the dot product of each with k ....
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