$\"\"$

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Radius of the Ferris wheel is $\"\"$ m.

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Ferris wheel is rotating at a rate of one revolution for every $\"\"$ minutes.

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Let the angle of elevation from the center at any time $\"\"$ is $\"\"$ .

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One revolution gives $\"\"$ radians.

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Ferry wheel makes one revolution for $\"\"$ minutes.

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That is $\"\"$ radians for $\"\"$ minutes.

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Therefore,

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$\"\"$

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Assume that the vertical height of the rider at any time $\"\"$ as $\"\"$ .

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$\"\"$

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Consider

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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When the height of the seat above the ground is $\"\"$ m, then

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$\"\"$

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Therefore, $\"\"$ .

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

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$\"\"$

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Speed of the rider when the height of the his seat above the ground is $\"\"$ m is $\"\"$ m/min.

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$\"\"$

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Speed of the rider when the height of the his seat above the ground is $\"\"$ m is $\"\"$ m/min.