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Math Help - Sinusoidal equation

  1. #1
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    Nov 2009
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    Question Sinusoidal equation

    A boat is tied up at a dock and bobs up and down. The vertical distance between its high and low point is 1.8 m and the cycle is repeated every 4s.

    a) Determine a sine equation to model the vertical position, in metres, of the boat versus the time, in seconds.

    b) Use your model to determine when, during each cycle, the boat is 0.5 above its mean position. Round your answers to the nearest hundreth of a second.
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  2. #2
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
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    Part a

    If the distance bet the two pts. is 1.8, then the amplitude of the sine equation is 0.9m. If the entire cycle is repeated every 4s, then the equation becomes

    x=0.9sin90t, where x is vertical height un metres.

    Part b

    Let x=0.5 and solve the equation.
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