College Algebra – Bouncing Ball Activity
Name: ___________________________________________
Name(s) of Other Group Member(s):_______________________________________________________
Objective: To use calculator regressions to determine and apply the relationship between the heights
of dropped balls and the heights of their bounces.
Materials: Yardstick, golf ball, ping-pong ball, tennis ball, graphing calculator
Step 1: Fill in the following tables by dropping tennis balls, ping-pong balls, and golf balls from
different heights and recording the height of one bounce. After completing five trails at each height,
find the average of all five trails, rounding to the nearest hundredth.
Tennis Ball
Drop
Height (x)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Average
Bounce (y)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Average
Bounce (y)
Trial 2
Trial 3
Trial 4
Trial 5
Average
Bounce (y)
6 in
12 in
18 in
24 in
30 in
36 in
Golf Ball
Drop
Height (x)
6 in
12 in
18 in
24 in
30 in
36 in
Ping-Pong Ball
Drop
Trial 1
Height (x)
6 in
12 in
18 in
24 in
30 in
36 in
Step 2: With the initial drop height as the independent variable (x) and the average bounce-back as
the dependent variable (y), use a graphing utility to determine the function of best fit for each type of
ball. Write your equations in the spaces provided, rounding to the nearest thousandth.
Tennis Ball: ________________________________________
Golf Ball: ________________________________________
Ping-Pong Ball: _____________________________________
Discussion/Questions – Read each question thoroughly and answer each part
1. Interpret the y-intercept for the equations above (answer is same for each type of ball). Does each of
these values seem reasonable in the three equations above? Why or why not?
2. Interpret the slope for the equations above (answer is the same for each type of ball). What do
larger slopes mean? What would a slope greater than one represent?
Disclaimer: In the questions below, ignore aspects such as wind resistance, terminal velocity, etc.
3. If a tennis ball had a bounce of 200 inches, from what height was it initially dropped? Show all work.
4. If you were to drop a golf ball from the top of the Empire State Building (1453 ft), how high would it
bounce? Show all work.
5. If all three balls were dropped from the top of the London Eye (443 ft), which (if any) would bounce
higher than Big Ben (316 ft)? Show all work.
6. If a ping-pong were dropped from a height of 1000 inches, what would be the height of its third
bounce? Show all work.