to fall this distance. The bungee slows her down at this point, so the fastest she is moving is . (I can show you how do derive these formulas if you like.)
Now, she starts out at 20 m with her highest speed and ends at 48 m with a speed of 0. This is going to represent 1/4 of the cycle of a cosine function. This cosine function takes the form:
where , A is the amplitude of the "wave" which is 48 m - 20 m = 28 m, and is the angular frequency of the oscillation of her motion on the bungee. The amount of time it takes for one period of the motion is given by , or
Now, is given by the spring equation by
where k is the spring constant of the bungee cord and m is the mass of the diver. As we are given neither of these data we cannot finish the problem.
We can, of course, give it in its form depending on k and m, though. The time it takes for the diver to fall from where the bungee starts to retard her motion to her lowest point is
So the total time for the fall will be