Question

Geometric Series Help

Answer 1

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. Drop the ball close enough to the measuring tape to be able to record height, but not touch the tape.
4. 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.)
illustration showing a ball bouncing 4 times if someone dropped the ball from 7 or 8 feet high


Note: The ball should bounce vertically and you want to measure the maximum height of each bounce. This image is to show you the ball bouncing.
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
Height 1 72 72
(starting point)
Height 2 42 46
Height 3 27 23
Height 4 20 12
Height 5 15 7
6. Repeat the process with each ball. Be sure that each ball is dropped from the same original height.
7. Using complete sentences, answer the following questions:
A. 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.
B. How does the size of the ball affect the height the ball bounces? Does the size have any effect on the common ratio?
C. If ball 1 were dropped from a different height, would the common ratio be different? Explain your reasoning.
D. What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn – 1 and show your work.
E. What is the total distance of the height each ball has traveled in the first five heights? Use the geometric series formula, Sn = 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.

Answer 2

Is the Equation not working today?

Answer 3

@agent0smith @ganeshie8

Answer 4

I have already done 1-6 it is the questions on #7 I am having trouble with.

Answer 5

avg common ratio is fraction between heights of consecutive bounces
height2/height1 or height3/height2

for example for ball1 you would compute:
42/72
27/42
20/27
15/20

then take avg value and call that the common ratio for ball 1

to find height 6 you would simply multiply 15 by this ratio

Answer 6

the initial height has no bearing on the common ratio between the heights of consecutive bounces

Answer 7

The common ratio would be .543384 right?

Answer 8

Would you divide the values added together by 4 or 5?

Answer 9

4 because there are 4 fractions

Answer 10

should be closer to .75

Answer 11

Dividing by 4 I got .67922875

Answer 12

yep

Answer 13

And for ball 2 .635985. So would ball 1 be decreasing height by 67.9% each time and ball 2 by 63.6%.

Answer 14

yes, those numbers will represent "r" in the geometric formulas

Answer 15

Ok thank you so much! I think I can do the rest now. :)

Answer 16

For a1 would I use the starting height or the height of the first bounce?

Answer 17

starting height

Answer 18

Thank you very much for all your help!