06-24-2012, 04:20 PM

You will need the following materials:

â€¢three different balls of various sizes and textures

â€¢measuring tape or yardstick

â€¢a blank wall

â€¢a step stool or chair

â€¢a family member or friend

Procedure:

1.Choose a height from which all of the balls will be dropped one at a time.

2.Vertically along the blank wall, set up the measuring tape and step stool or chair.

3.Have a family member or friend stand on a step stool and drop one of the balls from the chosen height away from the measuring tape.

4.Face the measuring tape, opposite the ballâ€™s starting point from about 7 or 8 feet. As the ball falls, measure the height of the ball on four consecutive bounces. (You may need to repeat the process to ensure that your measurements are accurate. You may choose to video each drop to assure accuracy.)

5.Write the height of each bounce, beginning with the height from which the ball originally fell,

in the chart below.

Ball 1

Description:Ball 2

Description:Ball 3

Description:

Height 1

(starting point)

Height 2

Height 3

Height 4

Height 5

6.Repeat the process with each ball. Be sure that each ball is originally dropped from the same height.

7.Beginning with Height 1, plot the height number (1, 2, 3, â€¦) on the x-axis and the corresponding height measurement on the y-axis in GeoGebra. You may do this by using the â€œNew Pointâ€ icon at the top of the screen or by typing each ordered pair in the â€œInput Boxâ€ at the bottom of the screen.

For example, if you dropped the ball from a height of 12 feet, the first point you would plot is (1, 12).

Be sure that you can see each point on the screen. You may need to alter the range of numbers on the x- and y-axes, by accessing the â€œGraphics Viewâ€ from the â€œOptionsâ€ menu.

8.Once the points have been plotted, draw the function which will closely connect them by using the command â€œFitExp.â€ Type FitExp[ followed by each ordered pair from the chart, separated by a comma. Finish the command with a closed bracket ]. An abbreviated example is shown below.

Repeat this procedure for each of the three balls. In the end, you will have a coordinate plane with three different graphs.

9.Identify the functions that have been graphed on the left side of the screen in the Algebra Window for each graph.

10.Using complete sentences, answer the following questions:

â€¢What is the common ratio between the successive height values of ball 1? Ball 2? Ball 3?

â€¢How does the size of the ball affect the height the ball bounces?

â€¢What affect, if any, does the size of the ball have on the common ratio?

â€¢If ball 1 were dropped from 2 feet higher, would the common ratio be different? Explain your answer.

â€¢What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn â€“ 1 and show your work.

â€¢What is the total distance of the height each ball has traveled? Use the geometric series formula, s_n=(a_1-a,r^n)/1-r and show your work.

â€¢three different balls of various sizes and textures

â€¢measuring tape or yardstick

â€¢a blank wall

â€¢a step stool or chair

â€¢a family member or friend

Procedure:

1.Choose a height from which all of the balls will be dropped one at a time.

2.Vertically along the blank wall, set up the measuring tape and step stool or chair.

3.Have a family member or friend stand on a step stool and drop one of the balls from the chosen height away from the measuring tape.

4.Face the measuring tape, opposite the ballâ€™s starting point from about 7 or 8 feet. As the ball falls, measure the height of the ball on four consecutive bounces. (You may need to repeat the process to ensure that your measurements are accurate. You may choose to video each drop to assure accuracy.)

5.Write the height of each bounce, beginning with the height from which the ball originally fell,

in the chart below.

Ball 1

Description:Ball 2

Description:Ball 3

Description:

Height 1

(starting point)

Height 2

Height 3

Height 4

Height 5

6.Repeat the process with each ball. Be sure that each ball is originally dropped from the same height.

7.Beginning with Height 1, plot the height number (1, 2, 3, â€¦) on the x-axis and the corresponding height measurement on the y-axis in GeoGebra. You may do this by using the â€œNew Pointâ€ icon at the top of the screen or by typing each ordered pair in the â€œInput Boxâ€ at the bottom of the screen.

For example, if you dropped the ball from a height of 12 feet, the first point you would plot is (1, 12).

Be sure that you can see each point on the screen. You may need to alter the range of numbers on the x- and y-axes, by accessing the â€œGraphics Viewâ€ from the â€œOptionsâ€ menu.

8.Once the points have been plotted, draw the function which will closely connect them by using the command â€œFitExp.â€ Type FitExp[ followed by each ordered pair from the chart, separated by a comma. Finish the command with a closed bracket ]. An abbreviated example is shown below.

Repeat this procedure for each of the three balls. In the end, you will have a coordinate plane with three different graphs.

9.Identify the functions that have been graphed on the left side of the screen in the Algebra Window for each graph.

10.Using complete sentences, answer the following questions:

â€¢What is the common ratio between the successive height values of ball 1? Ball 2? Ball 3?

â€¢How does the size of the ball affect the height the ball bounces?

â€¢What affect, if any, does the size of the ball have on the common ratio?

â€¢If ball 1 were dropped from 2 feet higher, would the common ratio be different? Explain your answer.

â€¢What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn â€“ 1 and show your work.

â€¢What is the total distance of the height each ball has traveled? Use the geometric series formula, s_n=(a_1-a,r^n)/1-r and show your work.