Question 1119329
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The diameter is 59 meters and the bottom is 4 meters off the ground, so the center of the circle is at 29.5 + 4 = 33.5 meters.  The amplitude of the sinusoidal variation is the radius, 29.5.  The period of revolution is 3 minutes, and one revolution is *[tex \Large 2\pi] radians.  So the radian measure of the rotation of the wheel at time *[tex \Large t] is *[tex \Large \frac{2}{3}\pi{t}].  The measurement of the height starts at one of the extremes, hence the cosine is the correct model.  Further, since it starts at the low extreme point, the opposite of the cosine must be used.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ h(t)\ =\ -29.5\cos\(\frac{2}{3}\pi{t}\)\ +\ 33.5]


The first time that the riders reach 18 meters is before they reach the maximum height of 63 meters at time 1.5 minutes.  The second time is between 1.5 minutes and the time they reach the low point again at 3 minutes.


Solve


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -29.5\cos\(\frac{2}{3}\pi{t}\)\ +\ 33.5\ =\ 18]


For *[tex \Large t] on the interval *[tex \Large 1.5\ <\ t\ <\ 3.0]


If you are using degrees instead of radians, *[tex \Large 1\text{ radian }=\ \frac{180}{\pi}\text{ degrees}]
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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