Tidal forces are greatest when the Eaetg, the sun and the moon are in line. When this occurs at the Annapolis Tidal Generating Station, the waterhas a maximum depth of 9.6 m at 4:30 pm and a minimum depthof 0.4 m 6.2 hourslater.
the equation is:
y= 4.6cos (2pi/12.4) (t-4.5) + 5
I don't know how the phase shift was determined.
What is the depth of the water at 9:30 am and 6:45 pm??
To determine the depth of the water at 9:30 am and 6:45 pm, we need to substitute the respective values of time into the equation:
For 9:30 am:
t = 9.5
y = 4.6 * cos(2π/12.4 * (9.5 - 4.5)) + 5
Simplifying further:
y = 4.6 * cos(2π/12.4 * 5) + 5
Evaluating the expression:
y ≈ 4.6 * cos(2π/12.4 * 5) + 5 ≈ 4.6 * cos(1.607) + 5 ≈ 4.6 * (-0.419) + 5 ≈ -1.93 + 5 ≈ 3.07 meters
So, the depth of the water at 9:30 am is approximately 3.07 meters.
For 6:45 pm:
t = 18.75
y = 4.6 * cos(2π/12.4 * (18.75 - 4.5)) + 5
Simplifying further:
y = 4.6 * cos(2π/12.4 * 14.25) + 5
Evaluating the expression:
y ≈ 4.6 * cos(2π/12.4 * 14.25) + 5 ≈ 4.6 * cos(8.65) + 5 ≈ 4.6 * (-0.785) + 5 ≈ -3.61 + 5 ≈ 1.39 meters
So, the depth of the water at 6:45 pm is approximately 1.39 meters.
To determine the depth of the water at different times, we need to substitute the respective time values into the given equation:
y = 4.6cos((2pi/12.4) * (t-4.5)) + 5
Let's calculate the depth of the water at 9:30 am (t = 9.5 hours):
y = 4.6cos((2pi/12.4) * (9.5-4.5)) + 5
= 4.6cos((2pi/12.4) * 5) + 5
≈ 4.6cos(2.01) + 5
≈ 4.6 * (-0.416) + 5
≈ -1.916 + 5
≈ 3.084
The depth of the water at 9:30 am is approximately 3.084 meters.
Next, let's calculate the depth of the water at 6:45 pm (t = 18.75 hours):
y = 4.6cos((2pi/12.4) * (18.75-4.5)) + 5
= 4.6cos((2pi/12.4) * 14.25) + 5
≈ 4.6cos(9.15) + 5
≈ 4.6 * (-0.991) + 5
≈ -4.558 + 5
≈ 0.442
The depth of the water at 6:45 pm is approximately 0.442 meters.
Therefore, the depth of the water at 9:30 am is approximately 3.084 meters, and the depth of the water at 6:45 pm is approximately 0.442 meters.
In your equation, t is the number of hours past noon.
At 9:30 AM, use your equation with t = -2.5 (hours)
At 6:45 PM, use your equation at 2.25 h.
Cosine function fits to tidal variations, such as this, are not good for much more than 12 hours. The amplitude is constantly changing.