That Is the Way the Ball Bounces!

Sam completed the following procedure in his Algebra II class:

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.) 
   
   
   
   
   

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   He recorded 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)	3 ft	3 ft	3 ft
   Height 2	2.4	1.9	0.9
   Height 3	1.9	1.2	0.3
   Height 4	1.5	0.8	0.1
   Height 5	1.2	0.5	0.02

   
   
   Using complete sentences, answer the following questions:
1. 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.
2. 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.
3. 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.

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