Math 115: Project 1

(See the Team work guide on the class web page)

One of the great remaining frontiers that need exploring on Earth is its oceans. Over half of the population on this planet lives within 100 miles of an ocean, so oceans play a significant role in human society. Tidal flow is part of the daily dynamics that affects the coastal zones. This is especially apparent in the Bay of Fundy in Nova Scotia which has the largest tides in the world. The difference between low and high water levels is 15 meters (nearly 50 feet). The time between successive tides is 12.4 hours.

At a particular point, the depth of the water, y meters, is given as a function of time, t, in hours since midnight by the function

y = D + A cos(B(t-C)).

(a) Draw some possible graphs of the function for y. Discuss how your graphs match the data given above.

(b) What is the physical meaning of D?

(c) What is the value of A?

(d) What is the value of B?

(e) What is the physical meaning of C?

(f) Using appropriate values for A,B,C and D and your graphing calculator, draw a possible graph for the function y.