Rate of change in distance question

  1. Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back.
    (In case you're wondering, I'm doing my studies by correspondence, so other than course notes and textbooks borrowed from the library I have just the internet and my brains (hah!) to aid me)

    1. The problem statement, all variables and given/known data
    A baseball diamond has sides 27m long. A player is running from 2nd to 3rd at a speed of 9m/s. When he is 6m away from 3rd, at what rate is the player's distance from home plate changing at that instant?


    3. The attempt at a solution
    x = distance from home plate to 3rd = 27m
    y = distance from player to 3rd = 6m
    z = distance from player to home = 27.66m (using pythagoras)
    speed of player is change of y over time: dy/dt = 9m/s

    [tex]z^{2}[/tex] - [tex]y^{2}[/tex]= [tex]x^{2}[/tex]
    differentiate with respect to time:
    d/dz[tex]z^{2}[/tex] - d/dy[tex]y^{2}[/tex]= 0 (since x doesn't change over time)

    dz/dt*2z - dy/dt*2y = 0
    divide by 2:
    z*dz/dt - y*dy/dt = 0
    sub the above (z, y, dy/dt) into the equation and solve:
    dz/dt = 1.95m/s

    If this ain't correct, please tell me quickly as I need to post my assignment off asap!
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,043
    Science Advisor
    Homework Helper

    Hi Dr Zoidburg! :smile:

    Yes, that's fine (but a little messy)! :smile:

    Try shortening it a bit.

    For example, there's no need to define an x (I know it's useful for helping you get to your eureka moment, but once you're there, you can forget it) … just say z² = y² + 729 (or z = √(y² + 729)). :smile:

    And
    doesn't make sense, does it? :rolleyes:
     
  4. yay, got it right! Off to the post office I scurry.

    And that other bit just came out poorly due to bad formating. It looks better in my assignment :wink:
     
  5. tiny-tim

    tiny-tim 26,043
    Science Advisor
    Homework Helper

    :smile: I thought Dr Zoidburg scuttled ? :smile:
     
  6. whoops. you're right there. scuttled. whoop! whoop! whoop!

    "Friends, help! A guinea pig tricked me!"
     
  7. tiny-tim

    tiny-tim 26,043
    Science Advisor
    Homework Helper

    I just did a google search for "A guinea pig tricked me",

    :biggrin: and got 5370 hits! :biggrin:
     
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