Math 4713

Part Four—Middle Grades Majors

How high will a ball bounce?

Introduction:

Question: If you drop a ball from 50 feel, how high will it bounce on the first bounce?

What are some things that might affect how high a ball bounces?

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Suppose you drop a tennis ball from 50 feet. How high do you think it will bounce on the first bounce? Record your guess here.___________________________________

Data Collection:

You will be working with a partner to gather your data. One person will need to be the “dropper.” This person will measure the height of the ball from the floor and will also drop the ball. The other person will be the “eye-baller.” This person will need to visually determine the height of the ball after the first bounce.

• Dropper: Measure 12 inches from the floor to the bottom of the ball. Drop the ball from this height.
• Eye-baller: Estimate the height of the ball after the first bounce. Record this in the data chart.
• Repeat this process two more times with the ball 12 inches from the floor and record the bounce heights.
• Continue to drop the ball 3 times for each of the remaining heights in the data chart and record the corresponding bounce heights.

Data Entry:

• Open the Fathom software on a PC with your partner.
• Click and drag the New Case Table icon onto the blank worksheet.
• Click on <new> and type: drop_height
• Hit enter.
• Click on <new> and type: bounce_height
• Hit enter.
• Double click on Collection 1 insides the box to rename the collection, then type: Bouncing Ball.
• Click on the box under drop_height and enter the drop heights, hitting enter after each entry.
• Click on the box under bounce_height and enter the corresponding bounce heights, hitting enter after each entry.

Graphical Representations of the Data:

You are going to create a scatter plot of your data.

• Click on the new graph icon and drag it to an open place on the worksheet.
• Grab and drop the drop_height title from the case table to the graph where it says, “Drop an attribute here.”
• Grab and drop the bounce_height title from the case table and drop it on the vertical axis of the graph. You will know that you are ready to drop the attribute title when the vertical axis is bold.

Discussion:

• Provide a description of your scatter plot. What is happening to the bounce height as the drop height increases?

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The Movable Line:

Use Fathom’s movable line feature to position a line on the scatter plot that “fits” the data.

• With the graph selected, click on Graph and the Movable Line. A line will appear on your scatter plot. Notice that the equation of this line is given at the bottom of the scatter plot.
• To move the line up and down, place your cursor on the middle of the line. When the cursor turns into a double arrow, click and drag to move the line.
• To change the slope of the line, place your cursor on either end of the line. When the cursor turns into a curved double arrow, click and drag to move the line.
• Continue to move the line until you feel that your line “fits” the data. Record the equation of your line here.__________________________________

How high will the ball bounce?

The equation of your movable line can now be used to predict how high the ball will bounce if dropped from 50 feet.

• Substitute 50 in the equation for the variable “drop_height.” Then solve the equation for the variable “bounce_height.” Show your work below.

• Complete the following: If this ball is dropped from 50 feet above the ground, it will bounce__________________________feet on the first bounce.

Discussion:

• Compare your initial guess to the answer you just computed.
• Was your initial guess close to the answer?
• Did you overestimate or underestimate the bounce height?

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• Why do you believe your results are different from your prediction?

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• Write a few sentences describing what you found in this activity.

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Before closing your Fathom file, be sure to save your work. Save your work as bouncing_ball.ftm onto your floppy disk in drive A.

How high will a ball bounce?

Data Sheet

Drop Height (in inches)	Bounce Height (in inches)
12
12
12
18
18
18
24
24
24
30
30
30
36
36
36
42
42
42
48
48
48
54
54
54
60
60
60