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A Ferris wheel has a maximum height of 56 m and a minimum height of 14 m.  It can make one rotation in 45 seconds.  During the first rotation, when is the instantaneous rate of change of the height of a chair on the Ferris wheel 0, if it starts at the height of the Ferris wheel’s axle?

 Dec 2, 2021
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This is not really a trig question. It is an understanding question.

 

dH/dt will be 0 when the tangent to the circle is horizontal.  That is at the top and bottom.   (say 12oclock and 6oclock)

 

If is starts horizontal to the axis that is at  3oclock or 9 oclock.

 

So it must travel a quarter of a rotation to get to the top or the bottom,

 

45/4 = 11.25 seconds  then again at  11.25+22.5k  seconds      (where k is a positive integer)

 Dec 3, 2021

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