cybogix4Lv1

27 Mar 2022

Class work on using trigonometric Function to model cyclical behavior

Problem Set:

1. In the classic novel Don Quixote, the title character famously battles a windmill. In this problem, you will model what happens when Don Quixote battles a windmill, and the windmill wins.

Suppose the center of the windmill is 20 feet off the ground, and the sails are 15 feet long. Don Quixote is caught on a tip of one of the sails. The sails are turning at a rate of one counterclockwise rotation every 60 seconds.

 

A. Explain why a sinusoidal function could be used to model Don Quixote's height above the ground as a function of time.

B. Sketch a graph of Don Quixote's height above the ground as a function of time. Assume t = 0 corresponds to a time when he was closest to the ground. What are the amplitude, period, and midline of the graph?

C. Model Don Quixote's height $H$ above the ground as a function of time $t$ since he was closest to the ground.

D. After 1 minute and 40 seconds, Don Quixote fell off the sail and straight down to the ground. How far did he fall?