Unformatted text preview: latform making its overall height 136
feet. It completes two revolutions in 2 minutes and 7 seconds. Assuming that the riders are at the
edge of the circle, ﬁnd a sinusoid which describes the height of the passengers above the ground t
seconds after they pass the point on the wheel closest to the ground.
Solution. We sketch the problem situation below and assume a counter-clockwise rotation.3 θ Q h
3 Otherwise, we could just observe the motion of the wheel from the other side. 11.1 Applications of Sinusoids 749 We know from the equations given on page 627 in Section 10.2.1 that the y -coordinate for counterclockwise motion on a circle of radius r centered at the origin with constant angular velocity
(frequency) ω is given by y = r sin(ωt). Here, t = 0 corresponds to the point (r, 0) so that θ,
the angle measuring the amount of rotation, is in standard position. In our case, the diameter of
the wheel is 128 feet, so the radius r = 64 feet. Since the wheel completes two revolutions in 2...
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