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Math Help - Ferris wheel problem calculus

  1. #1
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    Ferris wheel problem calculus

    Hi, can someone help. A ferris wheel has a diameter of 40ft and its axle is 25 ft above the ground. Three seconds after it starts, your seat is at a high point. The wheel makes 3 rev/min. I know that the equation is 25 + 20cos(pi/10)(t-3). What is the fastest that the function changes? Where is the seat when the function changest the fastest? Please explain the last 2 questions.
    Last edited by pantera; November 3rd 2008 at 10:32 AM. Reason: Found answer.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by pantera View Post
    Hi, can someone help. A ferris wheel has a diameter of 40ft and its axle is 25 ft above the ground. Three seconds after it starts, your seat is at a high point. The wheel makes 3 rev/min. I know that the equation is 25 + 20cos(pi/10)(t-3). What is the fastest that the function changes? Where is the seat when the function changest the fastest? Please explain the last 2 questions.
    You have:

    \theta(t)=\frac{\pi(t-3)}{10}

    h(t)=25 + 20 \cos(\theta(t))

    The rate of change of height is h'(t) and you need to find the maximum of this

     <br />
h'(t)=20 \sin(\theta(t))\ \frac{d\theta}{dt}=2 \pi \sin(\theta(t))<br />

    and the maximum absolute value of this occurs when \theta=\pi/2 and \theta=3\pi/2

    CB
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