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Rate of change of distance from origin?

  1. Aug 17, 2008 #1
    1. The problem statement, all variables and given/known data

    A particle moves along the parabola [tex]y = 4x^{2} [/tex] such that it's x coordinate increases at a steady rate of 5 units/minute.
    How fast is the particle's distance from the origin changing when it is at the point (1,4)?

    2. Relevant equations

    3. The attempt at a solution

    I honestly have no idea how to start this problem. A couple of ideas that pop up in my head are to take the derivatives [tex]\frac {dx}{dt}[/tex] and [tex]\frac {dy}{dt}[/tex] and use them to take the derivative of the distance formula from the origin, but there is no t...

    I have no idea. Someone help get me started?
  2. jcsd
  3. Aug 17, 2008 #2


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    Homework Helper

    Go with that thought. You have two pieces of information:
    the distance of a point (x,y) from the origin is given by [tex]s^2 = x^2 + y^2[/tex] and the position of a point (x,y) on the parabola is (x, x^2).

    You will be interested in ds/dt. Differentiate the distance equation implicitly with respect to t after making the appropriate substitutions.

    If you haven't had implicit differentiation yet, no matter. Make the appropriate substitutions into the distance equation and you will have the distance as a function of x only, which you can then solve for s and differentiate with respect to t.
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