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Because of the gravitational attraction of the moon and the sun on the Earth, water in seas and oceans tend to rise and fall periodically corresponding to what is called high and low tides. In a typical situation, the time between two high tides is close to 12 hours. On a particular day in the winter in a Boston port, it was determined that high tide was at midnight with a water height of 9.9 feet. Low tide was determined to be at 6am with a water height of 0.3 feet. (a) Determine a sinusoidal model for the height of the water t hours after midnight. (b) To launch your boat from this port you need the water height to be at least 7.5 feet. Determine the time intervals during the day when you will be able to launch your boat.

Because of the gravitational attraction of the moon and the sun on the Earth, water in seas and oceans tend to rise and fall periodically corresponding to what is called high and low tides. In a typical situation, the time between two high tides is close to 12 hours. On a particular day in the winter in a Boston port, it was determined that high tide was at midnight with a water height of 9.9 feet. Low tide was determined to be at 6am with a water height of 0.3 feet. (a) Determine a sinusoidal model for the height of the water t hours after midnight. (b) To launch your boat from this port you need the water height to be at least 7.5 feet. Determine the time intervals during the day when you will be able to launch your boat.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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Because of the gravitational attraction of the moon and the sun on the Earth, water in seas and oceans
tend to rise and fall periodically corresponding to what is called high and low tides. In a typical
situation, the time between two high tides is close to 12 hours. On a particular day in the winter in
a Boston port, it was determined that high tide was at midnight with a water height of 9.9 feet. Low
tide was determined to be at 6am with a water height of 0.3 feet.
(a) Determine a sinusoidal model for the height of the water t hours after midnight.
(b) To launch your boat from this port you need the water height to be at least 7.5 feet. Determine
the time intervals during the day when you will be able to launch your boat.   

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