First High & Low Tide in Harbor: Water Depth at 12am & 6pm

In summary, the depth of the tide in a certain harbor is modeled by y=21-5cos pi t/6, where y is the water depth in feet and t is the time in hours. For a day where t=0 represents 12:00 midnight, the first high tide occurs when t=3 or 9 AM and the water depth is 16 feet. The first low tide occurs when t=9 or 3 PM and the water depth is 26 feet.
  • #1
TonyC
86
0
Suppose the depth of the tide in a certain harbor can be modeled by y=21-5cos pi t/6, whre y is the water depth in feet and t is the time in hours. Consider a day in which t=0 represents 12:00 midnight. For that day, when are the first high tide and the first low tide and what is the water depth at each time?
 
Physics news on Phys.org
  • #2
You have:
[tex]-1 \leq \cos \alpha \leq 1[/tex]
So what can you say about the [tex]y = 21 - 5 \cos \frac{\pi t}{6}[/tex]
Viet Dao,
 
  • #3
What are you looking for?
 
  • #4
Okay, when y is minimum, that means:
[tex] 5 \cos \frac{\pi t}{6}[/tex] is maximum.
So [tex] \cos \frac{\pi t}{6}[/tex] is maximum.
So y is minimum means that [tex] \cos \frac{\pi t}{6}[/tex] is maximum.
[tex]-1 \leq \cos \frac{\pi t}{6} \leq 1[/tex] so what t makes [tex] \cos \frac{\pi t}{6}[/tex] maximum?
Viet Dao,
 
  • #5
you can take the first derivitive and then find when it is 0 to tell you where your critical points are then use that to find the min and max
 

1. What causes the tides in a harbor?

The tides in a harbor are caused by the gravitational pull of the moon and the sun on the Earth's oceans. As the Earth rotates, the ocean waters are pulled towards the areas where the moon and sun are directly overhead, causing high tides. At the same time, there are low tides in the areas where the moon and sun are not directly overhead due to the water being pulled away.

2. Why does the water depth vary between high and low tide in a harbor?

The water depth in a harbor varies between high and low tide because of the changing distance between the Earth and the moon as well as the Earth and the sun. When the Earth and moon are closest to each other, the gravitational pull is stronger, causing higher tides. When they are furthest apart, the gravitational pull is weaker, resulting in lower tides.

3. How often do high and low tides occur in a harbor?

High and low tides occur twice a day in a harbor, typically every 12 hours and 25 minutes. This is because it takes approximately 6 hours and 12 minutes for the moon to move from directly overhead to directly overhead again, resulting in two high tides and two low tides in a 24-hour period.

4. Can the time of high and low tides in a harbor change?

Yes, the time of high and low tides in a harbor can change due to various factors such as the alignment of the moon and sun, the shape of the coastline, and the depth of the water. Additionally, the time of high and low tides can vary from day to day, so it is important to consult tide charts for accurate and up-to-date information.

5. How does the water depth at 12am compare to the water depth at 6pm in a harbor?

The water depth at 12am and 6pm in a harbor can vary depending on the specific location and conditions. In general, the water depth at 6pm tends to be higher than at 12am due to the alignment of the moon and sun, which can result in higher tides during the afternoon. However, this is not always the case and can vary depending on the tide cycle and other factors.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
1
Views
815
  • Introductory Physics Homework Help
Replies
5
Views
986
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Precalculus Mathematics Homework Help
Replies
16
Views
2K
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
27
Views
7K
  • Precalculus Mathematics Homework Help
Replies
3
Views
2K
Back
Top