Tides are cyclical phenomena caused by the gravitational pull of the sun and the moon. On a particular retaining wall, the ocean generally reaches the 3m mark at high tide. At low tide, the water reaches the 1m mark. Assume that high tide occurs at 12:00 pm and at 12:00 am, and that low tide occurs at 6:00pm and 6:00am. What is the height of the water at 10:30 am?
From 12PM to 12am = 12hrs.
From 12PM TO 10:30AM = 10.5 HRS.
h = (10.5 / 12)3m = 2.625m.
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To determine the height of the water at 10:30 am, we need to understand the tidal pattern throughout the day based on the provided information.
Given that high tide occurs at 12:00 pm and at 12:00 am, and low tide occurs at 6:00 pm and 6:00 am, we can make a few observations:
1. The tidal cycle is approximately 12 hours (from high tide to high tide or low tide to low tide).
2. Between high tide and low tide, there are approximately 6 hours and 30 minutes.
From this, we can deduce that the tidal pattern follows a sinusoidal curve that reaches its peak at high tide and its lowest point at low tide.
In this case, the difference between high tide and low tide is 3 meters - 1 meter = 2 meters.
To find the height of the water at 10:30 am, we need to calculate the time difference from the nearest high or low tide.
From 12:00 pm to 10:30 am, there is a time difference of 10 hours and 30 minutes, which is about 1.75 cycles (10.5 hours divided by the approximate tidal cycle of 6 hours).
Each cycle corresponds to a height difference of 2 meters. Therefore, we can calculate the height of the water at 10:30 am by subtracting the appropriate amount from the high tide level.
Starting from the high tide level of 3 meters, subtracting 1.75 cycles would give us:
3 meters - (1.75 cycles × 2 meters) = 3 meters - 3.5 meters = -0.5 meters.
Converting negative values to actual tide level, we can interpret -0.5 meters as 0.5 meters below the low tide mark.
So, at 10:30 am, the height of the water would be 0.5 meters below the low tide mark.