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Graphing Stories #1 Peicewise Linear

posted Sep 12, 2013, 6:33 PM by Taryn Delaney   [ updated Sep 16, 2013, 6:30 AM by ]
Scientists, Engineers and Mathematicians don't sit around and take math tests for a living.  They use math to make models of real things.  If you want to build a rocket, knowing it has to be "fast" doesn't cut it.  You've got to know exactly how fast you want it to climb and descend or it will probably end up as a really expensive fireball.

1) Today, we're going to think like engineers, and draw our own graphs of real life situations.
First, you need the notes & hw: Download them here.

2) Watch the following video (make sure you stop it at 1:08)  Watch it as many times as you want, but don't watch the answer part!

3) Describe this man's motion in words, then graph the story.
Homework:  Watch this new video (graphing stories #3) of a man climbing a ladder to answer the following questions:

It shows a man climbing down a ladder that is 10 feet high. At time 0 seconds, his shoes are at 10 feet above the floor, and at time 6 seconds, his shoes are at 3 feet. From time 6 seconds to the 8.5 second mark, he drinks some water on the step 3 feet off the ground. Afterward drinking the water, he takes 1.5 seconds to descend to the ground and then he walks into the kitchen. The video ends at the 15 second mark.

a. Draw your own graph for this graphing story. Use straight line segments in your graph to model the elevation of the man over different time intervals. Label your x-axis and y-axis appropriately and give a title for your graph. 

b. Your picture is an example of a graph of a piecewise linear function. Each linear function is defined over an interval of time, represented on the horizontal axis. List those time intervals.

c. In your graph in part(a), what does a horizontal line segment represent in the graphing story? 

d. If you measured from the top of the man’s head instead (he is 6.2 feet tall), how would your graph change?

e. Suppose the ladder is descending into the basement of the apartment. The top of the ladder is at ground level (0 feet) and the base at the ladder is 10 feet below ground level. How would your graph change in observing the man following the same motion descending the ladder? 

f. What is his average rate of descent between time 0 seconds and time 6 seconds? What was his average rate of descent between time 8.5 seconds and time 10 seconds? Over which interval does he descend faster? Describe how your graph in part a can also be used to find the interval during which he is descending fastest.