Question

The height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction 4 pi Over 5 EndFraction (t minus one-half)) + 12. What is the minimum height of the flag?

3 feet
9 feet
12 feet
15 feet

Answer 1

15 feet

Explanation:

See the attached graph. [y and x replace h and t in the given equation]

The are two ways to answer the question. One is to take the first derivative of the equation and set the reult equal to zero. The solutions represnet the points at which the slope of the line is 0 (i.e., where the line changes direction - at the top and bottom).

An easier way is to graph the equation and look for the maximum(s). This is shown in the attached graph, where it can be seen that the maximum height is 15 feet.