Data Collecting and Modeling

  • #1

Homework Statement


The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function h(t)= 5 sin 30 (t-5) + 7
(A) find max and min value for depth of water.
(B) what time is high tide? What time is low tide?
(C) what is the depth of the water at 9:00am?



Homework Equations




The Attempt at a Solution


(A) The maximum would be 12 because 5 + 7. The minimum would be 2 because 7-5.


However when it comes to questions b and c I have no idea what to do or where to even begin.
 

Answers and Replies

  • #2

Homework Statement


The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function h(t)= 5 sin 30 (t-5) + 7
(A) find max and min value for depth of water.
(B) what time is high tide? What time is low tide?
(C) what is the depth of the water at 9:00am?



Homework Equations




The Attempt at a Solution


(A) The maximum would be 12 because 5 + 7. The minimum would be 2 because 7-5.


However when it comes to questions b and c I have no idea what to do or where to even begin.
I've figured out c just really stuck on b.
 
  • #3
SammyS
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Homework Statement


The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function h(t)= 5 sin 30 (t-5) + 7
(A) find max and min value for depth of water.
(B) what time is high tide? What time is low tide?
(C) what is the depth of the water at 9:00am?

Homework Equations




The Attempt at a Solution


(A) The maximum would be 12 because 5 + 7. The minimum would be 2 because 7-5.


However when it comes to questions b and c I have no idea what to do or where to even begin.
What process did you use to get the answers to (A) ?

... and (C) ?
 
  • #4
What process did you use to get the answers to (A) ?
I added the a value and the c value to obtain my maximum and I subtracted my c and a value to get my minimum.
 
  • #5
SammyS
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I added the a value and the c value to obtain my maximum and I subtracted my c and a value to get my minimum.
That's fine.

Why does that work?

By the way, what is the answer to (C) ?
 
  • #6
That's fine.

Why does that work?

By the way, what is the answer to (C) ?
The answer to c is 11.3 because I just substitute 9 for t in the equation.
 
  • #7
SammyS
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I added the a value and the c value to obtain my maximum and I subtracted my c and a value to get my minimum.
That's fine.

Why does that work?
 
  • #8
That's fine.

Why does that work?
It works because
That's fine.

Why does that work?
It works because the vertical shift is constant and the midline. Therefore you add or subtract the amplitude from it to get your answer.
 
  • #9
SammyS
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It works because

It works because the vertical shift is constant and the midline. Therefore you add or subtract the amplitude from it to get your answer.
What is shifted vertically?

How is this related to the sine function?
 
  • #10
What is shifted vertically?

How is this related to the sine function?
The height (m) gets shifted vertically?
 
  • #11
SammyS
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What function is it that's shifted vertically?
 
  • #12
SammyS
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Maybe I should have asked something more obvious.

Can you solve ##\ 5 \sin (30 (t-5)) + 7 =12 \ ## for ##\ t\ ## ?
 
  • #13
Maybe I should have asked something more obvious.

Can you solve ##\ 5 \sin (30 (t-5)) + 7 =12 \ ## for ##\ t\ ## ?
Maybe I should have asked something more obvious.

Can you solve ##\ 5 \sin (30 (t-5)) + 7 =12 \ ## for ##\ t\ ## ?
yes you can. Wouldn't the answer be 5.5?
 
  • #14
SammyS
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yes you can. Wouldn't the answer be 5.5?
What are the units of the coefficient, 30 ?
 
  • #15
What are the units of the coefficient, 30 ?
Isn't the 30
What are the units of the coefficient, 30 ?
not sure but is degrees? 30 is k value
 
  • #16
Isn't the 30

not sure but is degrees? 30 is k value
I have figured it out I realized I calculated something incorrectly.
 
  • #17
SammyS
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Isn't the 30

not sure but is degrees? 30 is k value
Right. Well then, actually it's 30 degrees per hour .

sin(θ) is a minimum (-1) or maximum (+1) at θ = -90° or 90° respectively ... of course ± integer multiples of 360° .
 

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