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Data Collecting and Modeling

  1. May 9, 2016 #1
    1. The problem statement, all variables and given/known data
    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?



    2. Relevant equations


    3. 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.
     
  2. jcsd
  3. May 9, 2016 #2
    I've figured out c just really stuck on b.
     
  4. May 9, 2016 #3

    SammyS

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    What process did you use to get the answers to (A) ?

    ... and (C) ?
     
  5. May 9, 2016 #4
    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.
     
  6. May 9, 2016 #5

    SammyS

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    That's fine.

    Why does that work?

    By the way, what is the answer to (C) ?
     
  7. May 9, 2016 #6
    The answer to c is 11.3 because I just substitute 9 for t in the equation.
     
  8. May 9, 2016 #7

    SammyS

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    That's fine.

    Why does that work?
     
  9. May 9, 2016 #8
    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.
     
  10. May 9, 2016 #9

    SammyS

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    What is shifted vertically?

    How is this related to the sine function?
     
  11. May 9, 2016 #10
    The height (m) gets shifted vertically?
     
  12. May 9, 2016 #11

    SammyS

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    What function is it that's shifted vertically?
     
  13. May 9, 2016 #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\ ## ?
     
  14. May 11, 2016 #13
    yes you can. Wouldn't the answer be 5.5?
     
  15. May 11, 2016 #14

    SammyS

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    What are the units of the coefficient, 30 ?
     
  16. May 11, 2016 #15
    Isn't the 30
    not sure but is degrees? 30 is k value
     
  17. May 11, 2016 #16
    I have figured it out I realized I calculated something incorrectly.
     
  18. May 11, 2016 #17

    SammyS

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    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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