Modeling Real Life Situations

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Modeling Real Life Situations

• Problem 2 Ferris Wheel

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• 2. As you ride the Ferris wheel, your distance
  from the ground varies sinusoidally with time.
  When the last seat is filled and the Ferris wheel
  starts, your seat is only part of the way up. You
  find that it takes 3 seconds to reach the top, 43
  feet above the ground, and that the wheel makes a
  revolution once every 8 seconds. The diameter of
  the wheel is 40 feet.

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A. Draw a diagram and graph of the solution.
1 rev 8 sec
3 sec to reach top
40 ft
Diameter 40 ft
3 ft
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B. What is the lowest you go as the Ferris wheel
turns, and why must this number be greater than
zero?

• 3 ft, because the diameter of the wheel is 40 ft,
  and the highest point is 43 ft, so the lowest
  point would be 3 ft (43-403)

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C. Create a Cos function in our form of y
ACosB(t-C)D

• Y 20Cos(p/4(t-3))23

8 seconds
43 ft
3
7
11
23 ft
1
5
9
3 ft
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D. Predict your height above the ground when t6,
t4 1/3, t9, and t0

• Y20Cos(p/4(6-3)23
• Y 8.857864376
• Y20Cos(p/4(4 1/3 -3))23
• Y29.36825196
• Y20(Cos(p/4(9-3))23
• Y3
• Y20(Cos(p/4(0-3))23
• Y 8.857864376

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E. What do you have to assume about the operation
of the Ferris wheel to make this an excellent
Cosine model?

• We have to assume that the Ferris wheel is
  constantly rotating without starting or stopping.
  If it did it would change the speed of the
  rotation.

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• Modeling Real Life Situations

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