**8.04 Project**

FONTS

What is the average common ratio between the successive height values of ball 1? Ball 2? Experimental errors may cause common ratios to have some variances within the data for one ball. Use the average common ratio.

Ball 1 - (-10)

Ball 2 - (-15)

How does the size of the ball affect the height the ball bounces? Does the size have any effect on the common ratio?

If the ball is bigger than the height of the bounce would be shorter. If the ball is smaller than the height of the bounce would be higher.

If ball 1 were dropped from a different height, would the common ratio be different? Explain your reasoning.

Yes; If ball 1 was dropped from a different height than the common ratio would be different because the height is increased so the ratio would increase as well

My Chart: Tennis ball vs Volley ball

Volley ball

Materialsssssss

two different balls of various sizes and textures

measuring tape or yardstick

a blank wall

a step stool or chair

a family member or friend to drop the balls

**By: Gabriela Hajaistron**

Procedure

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

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

Have a family member or friend stand on a step stool and drop one of the balls from the chosen height. Drop the ball close enough to the measuring tape to be able to record height, but not touch the tape.

Face the measuring tape, opposite the ball's starting point from about 7 or 8 feet high. As the ball falls, measure the height the ball reaches after each bounce for 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.)

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

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

Using complete sentences, answer the following questions:

What is the average common ratio between the successive height values of ball 1? Ball 2? Experimental errors may cause common ratios to have some variances within the data for one ball. Use the average common ratio.

How does the size of the ball affect the height the ball bounces? Does the size have any effect on the common ratio?

If ball 1 were dropped from a different height, would the common ratio be different? Explain your reasoning.

What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, a_n = a1r^(n – 1) and show your work.

What is the total distance of the height each ball has traveled in the first five heights? Use the geometric series formula, Sn=a_1-a_1r^n/1-r the quantity of a sub 1 minus a sub 1 times r to the n power, all over 1 minus r and show your work.

Height 1

Height 2

Height 3

Height 4

Height 5

84

84

Tennis Ball

74

64

54

44

69

54

39

24

What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, a_n = a_1r^n – 1 and show your work

the 6th height of the Tennis Ball would be 34in and the height of the Volley Ball would be 9in.

What is the total distance of the height each ball has traveled in the first five heights? Use the geometric series formula, S_n = a_1r^2/1 – r and show your work.

The total distance the Tennis Ball was 21.3333ft and the total for the Volley Ball was 22.5ft.

What did you think of this activity

What did you learn?

What possible errors could have altered your data?

Conclusion:

i could have missed judged where the ball dropped

I learned that sometimes to find the Geometric Sequence, you dont need to use the formula

I thought it was fun and different. id rather do these kinds of activities than computer work all the time