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Optimization(?) Problem

  1. Dec 11, 2005 #1
    A particle is travelling along the postivie x axis at a constant speed of 5 units per second.

    a) Where is the point when its distance from the point (0, 1) is increasing at a rate of 4 units per second?

    b) Where is the point when its distance from the point (0, 1) is increasing at a rate of 6 units per second?

    I am completely stuck, I could use some hints, thanks!
  2. jcsd
  3. Dec 11, 2005 #2

    Tom Mattson

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    Gold Member

    Start by writing down a function for the distance between the particle and the point (0,1) as a function of time.

    And no, this is not an optimization problem.
  4. Dec 11, 2005 #3
    one sec i'll post some stuff i was trying, and the question isn't optimization but i'm not really sure how to classify it
  5. Dec 11, 2005 #4
    here is the diagram i have


    since the y coordinate is constant, dy/dx is zero
    dx/dt = 5, and ds/dt = 4

    so s^2 = (x - 0)^2 + (y - 1)^2
    after taking the derivative of s = sqrt(x^2 + (y - 1)^2 and putting in the y point as y = 0
    i get
    ds/dt = x *dx/dt / sqrt(x^2 + 1)

    which, solving for x after putting in the dx/dt and ds/dt gets
    x = 3/4
    y = 0

    as the point, is that correct?
  6. Dec 11, 2005 #5
    actually this would be a related rates problem then
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