$\"\"$ \ \

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The diameter of the ferris wheel is $\"\"$ . \ \

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Consider a horizontal line through the center of the wheel as the equilibrium line, then the amplitude is $\"\"$ . \ \

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The ferris wheel rotates $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ \ \

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$\"\"$ .

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The distance between ferris wheel and the ground is $\"\"$ . \ \

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An object that moves on a coordinate axis so that the distance $\"\"$ from its rest position at time $\"\"$ , then the function is $\"\"$ .

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Since $\"\"$ peaks at $\"\"$ if $\"\"$ and is at its lowest if $\"\"$ , $\"\"$ .

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When $\"\"$ , the rider should be $\"\"$ above the ground. \ \

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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The equation of the riders motion is $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ .

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The equation of the riders motion is $\"\"$ .