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Finding change in altitude, and speed in x direction and y direction

  1. Apr 3, 2014 #1
    1. The problem statement, all variables and given/known



    A crazed ostrich names rhomboid runs along a mountain path with coordinates given by
    r(t) = < e^t, e^-t, sqrt(2) t>

    B) what is the change in rhomboids altitude from t=0 to t= 10

    C) what is rhomboids speed in x direction when t=4

    D) what is rhomboids speed in y direction when t=4

    E) find a formula for the total distance traveled by rhomboid from t= 0 to t=4










    2. Relevant equations



    • integration
    •derivatives















    3. The attempt at a solution

    For part b) the first thing I thought to do was to integrate only the z component ( since it's height) and evaluate the integral from 0 to 10? Which I get 50*sqrt(2)

    C) for speed in x direction do I take the magnitude of the derivative of e^t then plug t=4?
    x'(t) = e^t
    ||x'(t)|| = e^t
    Plug in t=4 I get 54.6

    D) I do the same as C) only this time I use the y component ?
    ImageUploadedByPhysics Forums1396562712.766847.jpg
     
  2. jcsd
  3. Apr 3, 2014 #2

    haruspex

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    Why are you integrating? What kind of beast is the integral of a position with respect to time?
    Yes and yes.
     
  4. Apr 3, 2014 #3
    That's what my group thought that we had to integrate... So how would we find change in altitude then?
     
  5. Apr 3, 2014 #4

    Dick

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    Just find the change in the z coordinate betweent t=0 and t=10.
     
  6. Apr 3, 2014 #5

    Just by simply plugging it into the original Z coordinate?
     
  7. Apr 3, 2014 #6

    haruspex

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    Yes.
     
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