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Math Help - Implicit differentiation

  1. #1
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    Implicit differentiation

    Hi, just wondering if I got this one right.

    A circle is given by an equation (see image). The first task is to find y' and y'' in the point (0,0). This I have done. Using implicit differentiation I got:

    y'=2 and y''=-5

    Now, the second question reads:

    "The circle describes the path of a particle. In the point (0,0) its speed in the x-direction, dx/dt, is 2 m/s. Find the particle's speed in the y-direction and the total speed."

    My reasoning goes like this:

    Since y' in the point (0,0) is 2, the particle's speed in the y-direction is double that in the x-direction. Therefore it must be 4 m/s.

    The total speed (v) is the sum of the two vectors x and y, and can be found using Pythagoras:

    v^2=2^2+1^2

    v=√5

    Does this make sense to you, or am I way off?

    Thanks
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  2. #2
    A Plied Mathematician
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    I agree with everything up until this point:

    v^2=2^2+1^2.

    I think you meant to write

    v^2=4^2+2^2, right?
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    I agree with everything up until this point:

    v^2=2^2+1^2.

    I think you meant to write

    v^2=4^2+2^2, right?
    Yes, that's what I meant. Glad to see my logic was right. I had been mulling over this problem for a while now..
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  4. #4
    A Plied Mathematician
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    Ok, I think you're good to go on that one. Have a good one!
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