a. In the t-H plane, where t, H denote time and height, respectively, draw a curve through the points (0,2), (1.5, 12), (3, 22), (4.5, 12), which are the South, East, North, and West points on the Ferris wheel circle along its revolution. The curve should also pass through (6,2), when the revolution is completed This part of the curve is the relevant part for the problem. The rest of the sinusoid curve can be drawn by repeated reflection and translation along the t-axis of the above part.
b. H = 12 - 10*cos((2*Pi/6 * t). It's straightforward to verify that this curve passes through the S, E, N, W points mentioned in a. above. [The "6" in the formula comes from the period of revolution = 6 minutes. The formula can be derived by parameterizing the 6-o'clock point by the angle t its radius vector makes with the negative H-axis. The angle t measures time from start.]
c. H > 15 when t is in the closed interval [1.79, 4.2] (endpoints are approximate). This can be seen by setting H > 15 in b. above and solving the resulting inequality. Hence, the total time spent above H = 15 is the length of this interval, 4.2 - 1.79 = 2.5 seconds.
