A Ferris wheel is 26 meters in diameter and completes 1 full revolution in 16 minutes. revolves 1 meter ground A Ferris wheel is 26 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h (t) gives a person's height in meters above the ground t minutes after the wheel begins to turn. a. Find the amplitude, midline, and period of h (t). Enter the exact answers. Amplitude: A = Midline: h= Period: P = meters diameter meters minutes b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t = 0. Find a formula for the height function h (t). Hints: • What is the value of h (0)? • Is this the maximum value of h (t), the minimum value of h (t), or a value between the two? • The function sin (t) has a value between its maximum and minimum at t = 0, so can h (t) be a straight sine function? • The function cos (t) has its maximum at t = 0, so can h (t) be a straight cosine function? c. If the Ferris wheel continues to turn, how high off the ground is a person after 56 minutes?
A Ferris wheel is 26 meters in diameter and completes 1 full revolution in 16 minutes. revolves 1 meter ground A Ferris wheel is 26 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h (t) gives a person's height in meters above the ground t minutes after the wheel begins to turn. a. Find the amplitude, midline, and period of h (t). Enter the exact answers. Amplitude: A = Midline: h= Period: P = meters diameter meters minutes b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t = 0. Find a formula for the height function h (t). Hints: • What is the value of h (0)? • Is this the maximum value of h (t), the minimum value of h (t), or a value between the two? • The function sin (t) has a value between its maximum and minimum at t = 0, so can h (t) be a straight sine function? • The function cos (t) has its maximum at t = 0, so can h (t) be a straight cosine function? c. If the Ferris wheel continues to turn, how high off the ground is a person after 56 minutes?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A Ferris wheel is 26 meters in diameter and completes 1 full revolution in 16 minutes.
revolves
1 meter
ground
▬
A Ferris wheel is 26 meters in diameter and boarded from a platform that is 1 meter above the ground.
The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1
full revolution in 16 minutes. The function h (t) gives a person's height in meters above the ground t
minutes after the wheel begins to turn.
Enter the exact answers.
a. Find the amplitude, midline, and period of h (t).
Amplitude: A =
Midline: h=
Period: P =
meters
diameter
meters
minutes.
b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel
starts spinning at time t = 0. Find a formula for the height function h (t).
Hints:
• What is the value of h (0)?
• Is this the maximum value of h (t), the minimum value of h (t), or a value between the two?
• The function sin (t) has a value between its maximum and minimum at t = 0, so can h (t) be a
straight sine function?
• The function cos (t) has its maximum at t = 0, so can h (t) be a straight cosine function?
c. If the Ferris wheel continues to turn, how high off the ground is a person after 56 minutes?
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