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Math Help - Precalc - Trig help!

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    Precalc - Trig help!

    Imagine you are riding a 20 meter diameter Ferris wheel that is making three revolutions per minute.
    a. What is the linear Velocity?
    b. ...angular velocity?
    c. There are 8 equally spaced seats on the Ferris wheel, what is the arc length between two adjacent seats?
    d. Let H(t) = the height (in meters) at t seconds, where H(0) = 0.
    Locate position on Wheel for each time:
    0 | 2.5 | 5 | 7.5 | 10 | 12.5 | 15| 17.5 | 20

    I'm pretty sure I got a b and c, I just want to check my answers!
    I have no idea where to begin with d, please help.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Nrp88 View Post
    Imagine you are riding a 20 meter diameter Ferris wheel that is making three revolutions per minute.
    a. What is the linear Velocity?
    b. ...angular velocity?
    c. There are 8 equally spaced seats on the Ferris wheel, what is the arc length between two adjacent seats?
    d. Let H(t) = the height (in meters) at t seconds, where H(0) = 0.
    Locate position on Wheel for each time:
    0 | 2.5 | 5 | 7.5 | 10 | 12.5 | 15| 17.5 | 20

    I'm pretty sure I got a b and c, I just want to check my answers!
    I have no idea where to begin with d, please help.
    So what are your answers for b and c?

    You have an angular speed \omega. The center of the circle the motion in in is a distance y_0 (which is R in this case) above the ground. We can represent this using either the sine or cosine function. I am going to arbitrarily use the cosine function in this instance. We need to have y(t) = 0, so we need to make the phase angle for the cosine function \pi so that we have R~cos(\omega t + \pi) = -R. So you know that at time t the vertical component of the position vector is given by
    y(t) = y_0 + R~cos ( \omega t + \pi )

    -Dan
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