Suppose Jim travels 2.5 radians per minute as he rotates on a Ferris wheel. The

Question

Suppose Jim travels 2.5 radians per minute as he rotates on a Ferris wheel. The Ferris Wheel has a radius of 35 feet. a. As Jim travels for t minutes on the Ferris wheel, how many radians (6) does Jim sweep out? radians Preview b. Define a function v that defines Jim's vertical distance above the horizontal diameter of the Ferris wheel (in feet) in terms of the number of minutes elapsed, t, since Jim started to rotate counter-clockwise from the 3 o'clock position. Preview c. Define a function h that defines Jim's horizontal distance to the right of the vertical diameter of the Ferris wheel (in feet) in terms of the number of minutes elapsed, t, since Jim started to rotate counter-clockwise from the 3 o'clock position. Preview d. How long does it take Jim to complete one revolution on the Ferris Wheel? minutesPreview

Explanation / Answer

Speed =2.5 radians per minute

radius=35 feet

a.theta= time *speed = 2.5 t

b. Let the distance be d

d/r=sin t

d= r sin theta = 35 sin t

c. Let the distance be h

cos t = h/r

h = r cos t = 35 cos t

d . 1 revolution = 2 pi radians

theta= 2pi = 2.5t

t= 2pi/2.5 minutes

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