5. Milton is floating in an inner tube in a wave pool. He is 1.5 m from the bottom of the pool when he is at the trough of a wave. A stopwatch starts timing at this point. In 1.25 s, he is on the crest of the wave, 2.1 m from the bottom of the pool. a) Determine the equation of the function that expresses Milton's distance from the bottom of the pool in terms of time. b) What is the amplitude of the function, and what does it represent in this situation? c) How far above the bottom of the pool is Milton att = 4 s? d) If data are collected for only 40 s, how many complete cycles of the sinusoidal function will there be? e) If the period of the function changes to 3 s, what is the equation of this new function?

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Chapter17: Sound Waves
Section: Chapter Questions
Problem 17.62AP
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5. Milton is floating in an inner tube in a wave pool. He is 1.5 m from the
bottom of the pool when he is at the trough of a wave. A stopwatch starts
timing at this point. In 1.25 s, he is on the crest of the wave, 2.1 m from the
bottom of the pool.
a) Determine the equation of the function that expresses Milton's distance
from the bottom of the pool in terms of time.
b) What is the amplitude of the function, and what does it represent in this
situation?
c) How far above the bottom of the pool is Milton att = 4 s?
d) If data are collected for only 40 s, how many complete cycles of the
sinusoidal function will there be?
e) If the period of the function changes to 3 s, what is the equation of this
new function?
ANSWERS
5. a) Answers may vary. For example, d = -0.3 cos(144r)° + 1.8
b) amplitude: 0.3, height of crest relative to normal water level
c) 2 m
d) 16
e) Answers may vary. For example, d = -0.3 cos(120z)° + 1.8
Transcribed Image Text:5. Milton is floating in an inner tube in a wave pool. He is 1.5 m from the bottom of the pool when he is at the trough of a wave. A stopwatch starts timing at this point. In 1.25 s, he is on the crest of the wave, 2.1 m from the bottom of the pool. a) Determine the equation of the function that expresses Milton's distance from the bottom of the pool in terms of time. b) What is the amplitude of the function, and what does it represent in this situation? c) How far above the bottom of the pool is Milton att = 4 s? d) If data are collected for only 40 s, how many complete cycles of the sinusoidal function will there be? e) If the period of the function changes to 3 s, what is the equation of this new function? ANSWERS 5. a) Answers may vary. For example, d = -0.3 cos(144r)° + 1.8 b) amplitude: 0.3, height of crest relative to normal water level c) 2 m d) 16 e) Answers may vary. For example, d = -0.3 cos(120z)° + 1.8
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