SOLUTION: A Ferris wheel with a diameter of 59 meters rotates at a rate of 3 minutes per revolution. Riders board the Ferris wheel 4 meters above the ground at the bottom of the wheel. A cou

Question 1119329: A Ferris wheel with a diameter of 59 meters rotates at a rate of 3 minutes per revolution. Riders board the Ferris wheel 4 meters above the ground at the bottom of the wheel. A couple boards the Ferris wheel and the ride starts.
Write a formula for the height of the couple t seconds after the ride begins.
How many seconds after the ride starts will the couple be 18 meters above the ground for the second time?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

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

radians. So the radian measure of the rotation of the wheel at time

. 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.

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.

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