Josie is sitting on a Ferris wheel. She is exactly 36 feet from the center and i

Question

Josie is sitting on a Ferris wheel. She is exactly 36 feet from the center and is at the 3 o'clock position when the Ferris wheel begins moving.

a. Suppose Josie has rotated 1.5 radians around the Ferris wheel (starting at the 3 o'clock position). How high is Josie above the horizontal diameter (in feet)?

b. Suppose Josie has traveled 272 feet from the 3 o'clock position. How high is Josie above the horizontal diameter (in feet)?

c. Define a function f that determines Josie's vertical distance above the horizontal diameter (in feet) as a function of the arc length (in feet), s , swept out by the Ferris wheel as it moves counter-clockwise from the 3 o'clock position.

Explanation / Answer

a) She has moved 3.1 radians

So, vertical distance travelled = radius*sin(angle rotated)

= 36sin(1.5) = 35.9 feet

b) Josie has traveled 272 feet from the 3 o'clock position.

Arc length =272 feet = radius*angle 'x' rotated

x*36 = 272 ----> x = 7.56 rad

Angle rotated above horizontal dia = 7.65 - 6.28 = 1.28 rad

So, vertical distance above horizontal dia. = 36sin1.28 = 34.48 feet

c)

Angle with the horizontal
A = arc/r = arc/36 (in radians)
Vertical distance from the center = 36*sin(A)
Vertical distance from the center = 36*sin(arc/35) = 36sin(s/36)

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