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??
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.
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.