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Math Help - particle velocity

  1. #1
    Junior Member winterwyrm's Avatar
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    particle velocity

    A particle is moving along the curve below. y= root(x)
    As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?

    I appreciate the help
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by winterwyrm View Post
    A particle is moving along the curve below. y= root(x)
    As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?

    I appreciate the help
    this is a related rates problem. did you draw a diagram? (see below). you want the rate at which z is changing. can you figure out a relationship to relate x, y and z?
    Attached Thumbnails Attached Thumbnails particle velocity-sqrt.gif  
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  3. #3
    Junior Member winterwyrm's Avatar
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    would it be pythagorean?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by winterwyrm View Post
    would it be pythagorean?
    indeed! so we will use z^2 = x^2 + y^2

    now what?
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  5. #5
    Junior Member winterwyrm's Avatar
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    Thanks! I know how to do the rest, take the derivative, plug in known variables, then it goes back to algebra 1-2. I just have alot of trouble making the proper equation.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by winterwyrm View Post
    Thanks! I know how to do the rest, take the derivative, plug in known variables, then it goes back to algebra 1-2. I just have alot of trouble making the proper equation.
    very good. when it comes to related rates, always draw a diagram if possible. as you can see, drawing that diagram allowed us to come up with Pythagoras' theorem as a way to relate the variables. if we had not drawn the diagram, we would probably not have known we were dealing with a triangle. so drawing the diagram is a good way to come up with what equation we should use, so remember that
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