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March 28, 2017

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You (safely) bungee jump from a 200-feet tall bridge in your town. Your distance above the water's surface depends on the time since you jumped. Sketch a reasonable graph.

  • Math:Trig.!!!! - ,

    at the beginning, till some time a,

    h(t) = 200 - 16t^2

    due to free-fall. When h(t) reaches 200 - max cord extension, the springy characteristics of the cord enter in. If the cord could rebound 100%, the wave would have a constant amplitude.

    for t>a,

    h(t) = b - c*cos(k(t-a))

    which allows for an offset cosine wave, starting at its minimum.

    However, the amplitude dampens exponentially, so the curve for t>a would more likely be something like

    h(t) = b - c*cos(k1(t-a))*e^(-k2*(t-a))

    So, a parabola to start with, then a damped cosine wave.

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