In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in June for Pensacola as a function of time (t) ...

Question

Physics

Giana Wang

18 July, 15:25

In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in June for Pensacola as a function of time (t) ...

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Fletcher Cruz · Answer 1

To answer this question, the equation that we will be using is:

y = A cos bx + c

where A = amplitude, b = 2 pi/Period, Period = 12 hrs, c = midline,

x = t and y = f (t)

A = 1/2 (Xmax - Xmin)

12 - 2 / 2 = 10/2 = 5

b = 2 pi / 12 = pi/6

c = 1/2 (Xmax + Xmin)

12+2/2 = 7

answer: f (t) = 5 cos pi/6 t + 7