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Math Help - Baseball diamond! (Calculus Help)

  1. #1
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    Baseball diamond! (Calculus Help)

    Hey everyone.

    I'm having a problem figuring out two problems that have to do with calculus... and baseball. :P

    Please help me with these two problems because I'm a little stuck in the middle with the first one.

    Here are the two problems:

    1. A baseball diamond has the shape of a square with sides 90 feet long. A player 30 feet from third base is running at a speed of 28 feet per second. At which rate is the player's distance from home plate changing?

    2. Now suppose the player is running from first to second at a speed of 28 feet per second. Find the rate at which the distance from home plate is changing when the player is 30 feet from second.

    If you decide to answer the whole problem, please explain how you get the answer. I want to try to study and learn how you get to the answer.

    Thanks a bunch, guys. This is urgent homework I have to get done. >.<

    Have a good one!

    -- RedSpades
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  2. #2
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    It's a toughy, I know.
    Anyone have any clue how to do this?
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  3. #3
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    It is a Pythagorean Theorem application.

    Right Triangle with sides 90 ft (third to home), 30 ft (running toward third), and the hypotenuse (distance from runner to home. Let's call this "Dist".)

    We have 90^{2} + 30^{2} = Dist^{2}

    Next, realize that everything is a function of time, in particular, we are given the shrinkage on the 30 ft side.

    90^{2} + [30 - 28*t]^{2} = Dist(t)^{2}

    The 90 ft side isn't changing until he rounds the corner, right?

    Okay, there is now an application of a derivative. What say you?
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