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Math Help - Need Help with Trig Modeling

  1. #1
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    Need Help with Trig Modeling

    Could someone help me with trig modeling problem?

    4)Assume that are aboard a submarine, submerged in the Pacific Ocean. At time t=0 you make contact with an enemy destroyer. Immediately, you start "porpoising" ( going deeper and shallower). At time t= 4 minutes, you are at your deepest, y= -1000 meters. At time t= 9 minutes, you next reach your shallowest, y= -200 meters. Assume that y vries sinusoidally with t for t > 0.
    a) Sketch the graph of y versus t.

    b) Write the particular equation expressing y in terms of t.

    c) Your submarine is "safe" when it is below y = -300 meters. At time t=0, was your submarine safee? Justify your answer.
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  2. #2
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    Trig equation

    Hello tictac
    Quote Originally Posted by tictac View Post
    Could someone help me with trig modeling problem?
    Quote Originally Posted by tictac View Post
    4)Assume that are aboard a submarine, submerged in the Pacific Ocean. At time t=0 you make contact with an enemy destroyer. Immediately, you start "porpoising" ( going deeper and shallower). At time t= 4 minutes, you are at your deepest, y= -1000 meters. At time t= 9 minutes, you next reach your shallowest, y= -200 meters. Assume that y vries sinusoidally with t for t > 0.
    a) Sketch the graph of y versus t.

    b) Write the particular equation expressing y in terms of t.

    c) Your submarine is "safe" when it is below y = -300 meters. At time t=0, was your submarine safee? Justify your answer.
    The equation you need will be something like

    y = a\sin b(t+c) +d

    In this equation, the amplitude = a = half the difference between the deepest and shallowest positions. (So you can work out the value of a, from the information given.)

    The period = \frac{2\pi}{b}= the time for one complete 'cycle' = twice the time between the deepest and shallowest positions. (So you can work out the value of b.)

    d represents the average depth; so it's mid-way between the deepest and shallowest. y then varies from d+a to d-a.

    c is the phase shift; you can work it out (once you've found a, b and d) if you know a value of y at a certain time t. So plug t = 4, y = -1000 into your equation, and you're there.

    Grandad
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  3. #3
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    Thumbs up Need help with Trig Modeling

    Thanks Grandad! I already solved it! The ans I got is:
    y = -400 sin (.628t -.943) - 600.


    Quote Originally Posted by Grandad View Post
    Hello tictacThe equation you need will be something like

    y = a\sin b(t+c) +d

    Thanks Grandad! I already solved it! The ans I got is:
    y = -400 sin (.628t -.943) - 600.


    In this equation, the amplitude = a = half the difference between the deepest and shallowest positions. (So you can work out the value of a, from the information given.)

    The period = \frac{2\pi}{b}= the time for one complete 'cycle' = twice the time between the deepest and shallowest positions. (So you can work out the value of b.)

    d represents the average depth; so it's mid-way between the deepest and shallowest. y then varies from d+a to d-a.

    c is the phase shift; you can work it out (once you've found a, b and d) if you know a value of y at a certain time t. So plug t = 4, y = -1000 into your equation, and you're there.

    Grandad
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