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Math Help - Applications of Derivatives help

  1. #1
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    Applications of Derivatives help

    A Ferris wheel with a 30 ft radius makes one revolution every 10 sec:
    a) Assume that the center of the Ferris wheel is located at the point (0,40), and write parametric equations to model its motion.
    b)At t=0 the point P on the Ferris wheel is located at (30,40). Find the rate of horizontal movement, and the rate of vertical movement of the point P when t=5sec and t=8 sec.

    For a, I think the answer is x=30cost, and y=30sint+40, since the radius is 30ft and it's center is at (0,40), but i think I'm wrong.
    For b, I'm not too sure. The concept of horizontal and vertical movement isn't clear to me, especially when t is a value.
    Please show work and have the answers, so I won't have to keep guessing, thank you.
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  2. #2
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    Quote Originally Posted by maximade View Post
    A Ferris wheel with a 30 ft radius makes one revolution every 10 sec:
    a) Assume that the center of the Ferris wheel is located at the point (0,40), and write parametric equations to model its motion.
    b)At t=0 the point P on the Ferris wheel is located at (30,40). Find the rate of horizontal movement, and the rate of vertical movement of the point P when t=5sec and t=8 sec.

    For a, I think the answer is x=30cost, and y=30sint+40, since the radius is 30ft and it's center is at (0,40), but i think I'm wrong.
    For b, I'm not too sure. The concept of horizontal and vertical movement isn't clear to me, especially when t is a value.
    Please show work and have the answers, so I won't have to keep guessing, thank you.
    you have to take the angular velocity, \omega , into account ...

    x = 30\cos(\omega t)

    y = 30\sin(\omega t) + 40

    where \omega = \frac{2\pi}{10} = \frac{\pi}{5}

    when t = 0 , point P is at x = 30 and y = 40

    when t = 2.5, point P should be at the very top of the wheel ... check it.

    to find the rates of horizontal and vertical motion, find \frac{dx}{dt} and \frac{dy}{dt} respectively and evaluate them at the requested times.
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    Can you explain to me how W equals pi/5?
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    Quote Originally Posted by maximade View Post
    Can you explain to me how W equals pi/5?
    \frac{1 \, revolution}{10 \, seconds} = \frac{2\pi \, radians}{10 \, seconds} = ?
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