# Rate of Change in a Wave Situation

A series of swells passes through a group of surfers. They notice that for a few minutes, the waves pass through at regular intervals: every 14 seconds. Let t=0 be the time when the wave is at its lowest point. The maximum instantaneous increase in height of the wave is 2.25 feet per second.

a. Find r(t), the rate of change of the height of the wave above the ocean floor at time t seconds.

b. If the bottom of the wave is 8 feet above the ocean floor, find h(t), the height of the wave at time t.

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...= A sin(2 Pi t / T)

with coefficient A determined by the specified maximum value, which happens at t = T/4, giving

2.25 ft/s = A sin(Pi/2)

and hence A = 2.25 ft/s, so

(t) = (2.25 ft/s)) ...