ACC. MATH II Name______
Ball Bounce Lab Period______Date______
Equipment: CBR
TI-83+/84 graphing calculator
TI link cable
Ball
1. Directions: Connect the CBR motion detector to the calculator through the IO port. If EasyData launches, locate the Set Up menu. Press the softkey below SetUp -- then choose “Ball Bounce” activity. Otherwise, press the [APPS] key, and scroll down to CBL/CBR – press [ENTER]. Choose the “RANGER” option, OR run the “RANGER” program that you downloaded earlier. Select “APPLICATIONS” and choose whatever units you would like to use. Then select “BALL BOUNCE”. In all cases, follow the directions on your calculator to set up the CBR.
2. Face the CBR toward the ground at a height of about six feet. Hold the ball under the CBR and drop it to watch it bounce. Follow the directions to get a good graph with at least 4 nice bounces. (If you are not satisfied with your graph, then choose to “REPEAT SAMPLE”.) Exit the CBL/CBR App by pressing [ENTER] and then “QUIT”. Press [GRAPH] to see your graph once again.
Examples: with
3. When you are satisfied with your collected data, sketch the Time-Distance plot from your calculator screen.
Xmin = ______
Xman =______
Ymin = ______
Ymax = ______
4. Using the TI-Link cable, [LINK] your data to the other members of your group, so that everyone has all four lists in case something gets erased accidentally.
(NOTE: Once every group has collected bounces, ask your teacher
to show everyone how to write a program to save this data!)
Part One (Ball Rebounding Factor) :
At this time, press [ENTER] and “QUIT” to leave the program. Use the [TRACE] feature of your calculator to help fill in the chart below. Let “Bounce Number 0” represent the height at which you let the ball go. (You can tell that by tracing the graph…)
Bounce Number (N) / Maximum Height (H)0
1
2
3
4
Plot the ordered pairs (Bounce Number,
Maximum Height), below. Be sure to label
your graph.
Do these points appear to be collinear? ______
They shouldn’t be, because theoretically they are points on an exponential function. Exponential functions have a common ratio instead of a common difference. Let’s see if your data shows that common ratio.
In the table to the right, calculate the ratio
of each maximum height to the maximum
height before it.
Do you think these ratios are approximately equal?
What is the average of these ratios?
This number should be the ratio we can use to find any rebound height.
If the ball was dropped from a height of 100 ft., use this ratio to find the height of the rebounding ball.
If this ball was dropped from a height of 600 cm, use this ratio to find the height of the rebounding ball.
Use any method you know to write the maximum height of the ball (H) as an exponential function of the bounce number (N).
Part Two (Distance-Time Graph): (Important – have you written your program to save data yet?)
1. The goal here is to “capture” one good parabolic bounce.
a. Press the [LIST] feature ([2nd] [STAT]), go to “OPS” and choose “SELECT(“. This will allow you to chop off a piece of your data. The “SELECT(“ will appear on your home screen, so you can decide where you want to put your list pieces. (I’d use the empty lists L5 and L6.) The calculator will then return you to the DIST-TIME graph where you may chop off a nice parabolic bounce.
b. Move the cursor to the left edge of a parabolic region of your choice.
c. Press [ENTER] to set the left boundary.
d. Now move the cursor to the right edge of that parabolic region.
e. Press [ENTER] to set the right boundary. After a moment you will see only the selected portion of the graph on the screen.
2. Now change your [STAT PLOT] to a scatter plot. Go to [2nd] [Y=] , open “Plot1”, choose the appropriate “Type”, and select as your “Mark” squares. (You may want to resize how big your graph is by going to [ZOOM] and choosing “ZoomStat”.) Trace to locate the vertex of the parabola and record the coordinates below. (You may interpolate to find the vertex if that would be more accurate than any of the actual data points you have.)
Time (s) / DistanceVertex:
Units you chose to use: ______
3. The goal here is to use “Trial and Error” to write an equation for this bounce. Remember that the vertex form of a parabola is , where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex of the parabola.
a. Since the parabola opens down, what do you know about a?______
b. Since you don’t know the exact value of a, let’s start with a = -1. Write the initial
guess for your equation of thee parabola in vertex form.
______
a. Press [Y=]. Enter your equation into Y1. Press [GRAPH]. You will discover that an a value of -1 does not fit this parabola. Press [Y=] , and enter a better guess for a. Press [GRAPH] again and see how this fits. Continue this process of refining a better guess for a until you have the best fit for the parabola. (You can also edit the coordinates of your vertex to produce a better fit.)
NOTE: If you have the TRANSFORM APP, turn it on, and type as your quadratic function. When you press [GRAPH] , you can change the values of a, c, and d on the screen and see the graph change interactively.
Record your value for a. ______
When you are completely satisfied with your parabolic fit, use TI-Connect to have the computer print this graph of the parabolic scatter plot and your equation. If you can’t print it out, take a picture of your calculator screen. (You’ll need to staple this to your lab when you turn it in.)
Questions:
A. What is the equation of the parabola that best fits this data?
______
B. What is your maximum value ? ______
C. What does this maximum value represent in relationship to the ball bounce?
______
D. Show work to expand your equation to write it in standard form.
______
Part Three (Calculator Regression Equation):
Now let the calculator find its equation of best fit: Press the [STAT] key and move the cursor over to “CALC”. Choose “5: QuadReg” and a menu should pop up. Fill in the location of your x and y values (L5 and L6?) and let the calculator store the equation in Y2. Then press [ENTER] to view the calculators result. Write that equation below.
______
Do you feel that your equation in standard form and the calculator’s regression equation are “close to the same”?______Why or why not?
Show work to find the vertex of the calculator’s equation.
Calculator’s vertex:______Your vertex:______
Is the calculator’s equation significantly better than the one you created?
Part Four (Velocity-Time Graph):
1. Re-enter the STAT PLOT by pressing [2nd] [Y=], and turn “Plot1” off. Go into “Plot2”, turn it ON, make it a scatter plot, and use L1 for x and L3 for y. For your [WINDOW], use the same Xmin and Xmax values as you used for your “nice bounce”, but you’ll need to set appropriate Ymin and Ymax values. (Remember that you can look at the numbers in L3 to decide what values are appropriate.)
2. [GRAPH] this new scatter plot. Does it appear to be linear, quadratic or exponential?
a. Go back to the [LIST] feature ([2nd] [STAT]), go to “OPS” and choose “SELECT(“ once again. This will allow you to again chop off a piece of your data to ‘clean it up’.
b. Move the cursor to the left edge of the linear graph using your cursor key. (Make sure to discard any horizontal portion of the line.)
c. Press [ENTER] to set the left boundary. Move the cursor to the right edge of the linear graph using the cursor keys. Press [ENTER] to set the right boundary. After a moment you will see the selected portion of the graph filling the width of the screen.
3. Record your graph below: Be sure to label it well.
4. Use the cursor to find and record the coordinates of two points that lie on the velocity graph.
Point 1: ______Point 2: ______
5. Show work to find the slope and y-intercept of this line.
m = ______b = ______
Record the equation of this line. ______
Questions:
A. Enter the equation above into the [Y=] line in Y2. Press [GRAPH]. How well does this line
fit the velocity data?
______
B. What does the slope of the line represent? ______
______
C. What is the relationship between the slope of the VEL-TIME graph and the leading
coefficient a of the DIST-TIME graph?
______
______
Overall: What did you learn from doing this lab?