Math - the Low and High Tides’ Height
Essay by Shuonan Yang • October 27, 2016 • Research Paper • 978 Words (4 Pages) • 989 Views
Task 2- Part 2
For 19th of September, the low and high tides’ height, and the time period of the tides are not consistent, thus, they need to be averaged to create a function.
Low tides (m) | High tides (m) | Time period between low tides | Time period between high tides | |
0.53 | 2.6 | 12hrs 21mins | 12hrs 10mins | |
0.77 | 2.52 | |||
Average | 0.65 | 2.56 | 12 hrs 15mins 30sec |
Let the model for 19th of September be a Cos graph.
A Cos B(x+C)+D
Average minimum height =0.65m
Average maximum height = 2.56m
Amplitute (A) = = = 0.955[pic 1][pic 2]
Average time period between the high and low tides 12hrs 16mins or hrs[pic 3][pic 4]
B= =[pic 5][pic 6]
C →since the model is a Cos graph, max =time at 0000 (12 am)
However, the 1st max occurs at 1112 on the 19th of September.
[pic 7]
D→if f(x)=0.955 Cos x, max = 0.955 min=-0.955
However, in this case, max= 2.56 min=0.65
Differences → max= 2.56-0.955 =1.605 min=0.65+0.955=1.605
[pic 8]
[pic 9]
, where t = time in 24hrs after the midnight on 19th of September.[pic 10]
One period (T)= max→ D→ min→ D→ max
12hrs 16mins = 3hrs 4mins[pic 11]
There is 3hrs 4mins difference between each point.
Starting from max at 1112,
D ← min ← D ← max → D → min → D → max
0200 0504 0808 1112 1416 1720 2024 2328
Clarity model: f(t)=A sin ( +B[pic 12]
Write the function in A Cos B(x+C)+D form: A sin +D[pic 13]
A= of the amplitude of [pic 14][pic 15]
=[pic 16]
D = =,5[pic 17][pic 18]
= (1.605)[pic 19][pic 20]
If, max=0.955 min=-0.955[pic 21]
However, max=0.546+1.204=1.75 min=-0.546+1.204=0.658[pic 22]
Time period between the high and low tides= = =30hrs[pic 23][pic 24]
One period (T)= D → max → D → min → D
30hrs = 7.5hrs[pic 25]
There is 7.5hrs difference between each point.
Starting from min at 1830,
D ← max → D → min → D
2000 (18/9) 0330 (19/9) 1100(19/9) 1830 (19/9) 0200(20/9)
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