Modeling Trigonometric Funtions

Question

The highest point on a a circular ferris wheel is 60 feet above the ground. the ride starts at the lowest seat on the wheel, which is 10 feet above the ground. It takes 12 seconds for you to reach the top. Write an equation of your height above ground as a function of time. Find your height above ground at 18 seconds, and 21 seconds. Find a time when you are exactly 50 feet above the ground.

Answer 1

Since it takes 12 seconds to travel half of the circle (180 degrees), you move thru 180/12 or 15 degrees/second, so after t seconds, the angle you've moved thru will be 15t degrees.

The height above the ground after t seconds will be the radius (30 feet) times the cosine of the angle moved thru for the first half of the trip and 30 plus the cosine of the angle moved thru - 90, so:

h = 30 * (cos 15t) for 0 <= t <= 6

and

h = 30 + (30 * (cos 15t - 90)) for 6 < t <= 12

Answering the rest of the question merely involves plugging in the values known and solving for what's not known.