Chapter 8 Project


Part I

In this chapter, we have given several examples of objects being dropped or propelled upward or downward. In this chapter project, we will use the TI-83 Plus and a Texas Instrument Calculator-Based Ranger (CBR) to collect our own data involving dropping and tossing a pillow. 


You will need the CBR, the Ranger program, and an object (a small pillow is easy to use).


1.         Run the Ranger program.

            a. Connect the CBR to the TI-83 Plus.

            b. Under programs, select RANGER.

            c. Under MAIN MENU, select 1:SETUP /SAMPLE

d. With the up or down arrow, select a line, and press image002 to change

the settings. The screen settings should read as follows:

           
            REAL TIME:        YES

            TIME(S):             15

            DISPLAY:           DIST

            BEGIN ON:        [ENTER]

            SMOOTHING:    NONE

            UNITS:                FEET


When the settings are correct, use the arrow to move the cursors to the top of the page, and

press image to start.

e. Press image002 to start the program.

f. Place the CBR on the floor.

g. Press image002 again to start data collection. The CBR will begin to make clicking noises.

The calculator will collect data points every 0.2 second.

h. From a height of about six feet directly above the CBR, drop a pillow on top of it.

i. When the data have been collected, press image002 to view the PLOT MENU. Choose

2:SELECT DOMAIN. You will be prompted to choose the left and right bounds of your data set.

 You will need to eliminate any points before the pillow dropped and after it hit the floor. You

may need to do this more than once. You may need to repeat the sample if your data do not

 appear to be correct. Press  image004  to exit. The calculator now has the time in seconds stored in

L1 and the distance above the CBR stored in L2.

j. Calculate the quadratic regression equation for your data. Use the data points to write a

quadratic function s(t) representing the height above the motion detector in feet, with t

representing the time after release of the pillow.


2. Repeat the steps in exercise 1, but this time, from a height of about 5 feet, toss the pillow upward so that it will fall on top of the motion detector. 

 

We have discussed the formula s(t) = -16t2 + v0 t + s0, where s(t) is the vertical distance in feet, t is time in seconds, v0 is the initial velocity, and s0 is the initial height. How do your two quadratic equations compare with this theoretical formula? Can you explain why your equation is not in this exact form? 


Part II


In this chapter, you encountered several exercises that used real data. For example, in Section 8.4, exercises 31 through 34 each ask you to write a quadratic function and predict future data. 

 

Search the internet or library for a similar set of data. List the source of your data. Use the data to write an exercise. Give enough information to write three data points, ask for a quadratic function to model the data, and ask for a prediction of future data.