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Applications of sinusoidal functions.

  1. Nov 1, 2011 #1
    1. The problem statement, all variables and given/known data
    At a seaport, the depth of the water h metres at time t hours during a certain day is given by this formula:

    Q: What is the maximum depth of the water? When does it occur?



    2. Relevant equations
    h = 1.8 sin 2pi [(t - 4)/12.4] + 3.1



    3. The attempt at a solution

    4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1
    1.8sin2pi = 0
    4.9 - 3.1 = (t-4)/12.4
    1.8 = (t-4)/12.4
    1.8 x 12.4 = t - 4
    22.32 + 4 = t
    26.32 = t

    That answer is wrong even when i convert from 24 hour clock to the 12 hour clock.
    The correct answer is 7:06a.m and 7:30a.m
     
    Last edited: Nov 1, 2011
  2. jcsd
  3. Nov 1, 2011 #2

    Mark44

    Staff: Mentor

    If the correct answers are 7:06am and 7:30am, what is the question? There is nothing in your problem statement that asks a question.
     
  4. Nov 1, 2011 #3
    Oops. Here's the question:


    Q: What is the maximum depth of the water? When does it occur?
     
  5. Nov 1, 2011 #4

    Mark44

    Staff: Mentor

    Why does the "correct" answer not give the maximum depth?

    And why is your first equation 4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1? Where did that 4.9 come from?
     
  6. Nov 1, 2011 #5
    Well the original equation is : h = 1.8 sin 2pi [(t - 4)/12.4] + 3.1
    Since it's a sinusoidal function, the maximum height of that this sinusoidal function can achieve is 4.9. You get that by adding 3.1 + 1.8 = 4.9

    And my first equation is 4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1 because I substituted the 4.9 as the y value since we want to find out what time the depth of the water is at its max (4.9)
     
  7. Nov 2, 2011 #6

    Mark44

    Staff: Mentor

    I think if you'll check the book, you'll find that you are missing some parentheses. This should be 4.9 = 1.8sin (2pi (t-4)/12.4]) + 3.1
    Then you should say something to establish this. The reason is that the maximum value of the sine function is 1, so the maximum value of 1.8*sin(whatever) + 3.1 is 4.9.
     
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