Bungee Barbie and Kamikaze Ken
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Bungee Barbie and Kamikaze Ken
Concepts
• Data gathering, display, analysis
• Linear regression
Materials
• 1 Barbie or Ken size doll or action figure per group of 3 or 4 students
• 40-50 rubber bands (2 one-pound boxes of 4-inch length unstretched) per group of 3 or 4
students
• Various weights such as washers, rolls of quarters, fishing weights, etc.
• Masking tape
• 2 meter sticks taped together for a diving board
• 9-inch by 13-inch pan of water
• 25-foot retractable tape measure
• TI-73 EXPLORER or TI-83 Plus/SE (one per group)
• Student activity sheet “Bungee Barbie and Kamikaze Ken”
Introduction
This activity is adapted from http://www.indiana.edu/~hmathmod/projects.html and engages teams
of students in simulating the testing of various drop heights for a bungee cord that optimizes the
thrill of splashing in a pool of water without incurring a head injury. Students use only one action
figure (doll) to determine for various heights above the floor the number of rubber bands that allows
their action figure to come as close to the floor as possible (for maximum thrills) without actually
hitting the floor.
Teams of 3 to 4 students have been hired to work for the Daredevil Adventure Company. This
company offers rock climbing, sky diving, "extreme skiing", and cliff diving adventures to the
public. To keep up with market demand, the company’s board of directors decided to add bungee
jumping to its offerings. Each team’s first assignment involves working with a group of three other
employees to determine the details of the new venture. The company has several sites planned for
bungee jumping and each site is at a different height.
Using only one action figure (doll), each team’s task is to determine for various heights above the
floor the number of rubber bands that allows their action figure to come as close to the floor as
possible (for maximum thrills) without causing any type of injury or fatality. Be aware that after
several uses the rubber bands will permanently deform or stretch and that this may affect the
problem. Let students discover and cope with this complication in any reasonable way (perhaps
using new rubber bands frequently or for the final test jump, or pre-stretching rubber bands).Bungee Barbie and Kamikaze Ken
Student Activity Sheet
Problem: You have been hired to work for the Daredevil Adventure Company. This company offers
rock climbing, sky diving, "extreme skiing", and cliff diving adventures to the public. To keep up
with market demand, the company’s board of directors decided to add bungee jumping to its
offerings. The company has several sites planned for bungee jumping and each site is at a different
height. Your first assignment involves working with a group of three other employees to simulate the
testing of the drop height for a bungee cord that optimizes the thrill of splashing in a pool of water
without actually hitting the floor. Using only one action figure (doll), your task is to determine for
various heights above the floor the number of rubber bands that allows your action figure to come as
close to the floor as possible (for maximum thrills) without causing any type of injury or fatality.
Step 1: Collecting the Data
If necessary, tape a weight to the doll’s back so s/he is heavy enough to stretch the bungee cord
(rubber band). You will need to do this if your dolls are lightweight or flimsy. Tie one rubber band
to the doll’s feet and drop it, head first, from various heights. Keep raising the jump height until the
ol’ coconut no longer hits the floor! Once you get close to this height, perform three trials and take
an average. Continue adding rubber bands and complete the table.
Number of Maximum Height You Can Safely Jump
Rubber Bands
Trial 1 Trial 2 Trial 3 Average
1
2
3
4
5
6
Step 2: Modeling the Data
Using your average heights, enter the Number of Rubber Bands data in one list and the Maximum
Height You Can Safely Jump data in another list. In the STAT PLOT Menu turn the plot on, select
the scatterplot option, use the Number of Rubber Bands data in the Xlist, and use the Maximum
Height You Can Safely Jump data in the Ylist. Adjust the window or select ZOOM 9: ZoomStat.
Graph the data. Use the STAT CALC menu to find a best-fit line that models the data.
Step 3: Using the Model and Analyzing Your Results
Each group performs a live demonstration at a different height to test the accuracy of their
prediction. A pan of water is on the floor directly below the launching board. You must find how
many rubber bands are needed so your action figure will get the biggest thrill without getting a
severe headache. Fasten the required number of rubber bands to your doll, and the entire group will
watch your doll’s jump. Your goal is to get a splash without a crash.
Presentation Requirements:
• Specify the prediction equation and verify through an actual demonstration.
• Identify any assumptions that were made.
• Include graphs and tables.
• Present methods of solution and justifications of conclusions.
• Include possible sources of error
PTE: Algebra Page 2
© 2003 Teachers Teaching With TechnologyBungee Barbie and Kamikaze Ken
Teacher Notes
Introduction
This activity engages teams of students in simulating the testing of various drop heights for a bungee
cord that optimizes the thrill of splashing in a pool of water without incurring a head injury. Students use
only one action figure (doll) to determine for various heights above the floor the number of rubber bands
that allows their action figure to come as close to the floor as possible (for maximum thrills) without
actually hitting the floor.
Teams of 3 to 4 students have been hired to work for the Daredevil Adventure Company. This company
offers rock climbing, sky diving, "extreme skiing", and cliff diving adventures to the public. To keep up
with market demand, the company’s board of directors decided to add bungee jumping to its offerings.
Each team’s first assignment involves working with a group of three other employees to determine the
details of the new venture. The company has several sites planned for bungee jumping and each site is at
a different height.
Using only one action figure (doll), each team’s task is to determine for various heights above the floor
the number of rubber bands that allows their action figure to come as close to the floor as possible (for
maximum thrills) without causing any type of injury or fatality. Be aware that after several uses the
rubber bands will permanently deform or stretch and that this may affect the problem. Let students
discover and cope with this complication in any reasonable way (perhaps using new rubber bands
frequently or for the final test jump, or pre-stretching rubber bands).
Instructions
Activity:
1. Find a location such as a stairwell, outside second story window, or location in a gymnasium
where the action figure can be dropped and enough room exists for the students to gather at the
base of where the doll will fall. Measure the distance from the floor to the launching board in
centimeters.
2. Give students the drop height, in centimeters, which Barbie or Ken will fall. Use a launching
board to ensure Barbie or Ken is level when s/he falls, and place a 9-inch by 13-inch pan
slightly filled with water below. You want splash but no crash. It is fun to videotape the
demonstrations, especially with a camcorder that can zoom-in on the pan of water.
3. Ask students to follow the activity sheet and create a model for their predictions.
4. Ask each group to give a presentation of their findings.
Presentation Requirements:
• Teams should be able to predict the length of rope for any given height using an equation.
Predictions will be verified through actual experimentation.
• Identify any assumptions that were made.
• Include graphs and tables.
• Present methods of solution and justifications of conclusions.
• Include possible sources of error.
Assessment:
1. Suppose one group draws a best-fitting line through their data points and finds that the
equation of their model is y = 29x+ 3.1, where x is number of rubber bands and y is the safest
PTE: Algebra Page 3
© 2003 Teachers Teaching With TechnologyBungee Barbie
height in centimeters that Barbie or Ken can be dropped. Use this equation to estimate the
amount of stretch (y-value) for 1 rubber band.
Answer: 29 cm. They must have some weights on the doll.
2. Using the model y = 29x+ 3.1, how many rubber bands would be required for your action
figure to safely drop a distance of 700 cm? What if you had to use a whole number of rubber
bands, i.e., no cutting?
Answer: Since x = 24.03, they might consider 24 rubber bands.
3. Using the model y = 29x+ 3.1, how many rubber bands would be required for your action
figure to safely drop a distance of 728 cm? What if you had to use a whole number of rubber
bands, i.e., no cutting?
Answer: Since x = 24.99, they might still try 24 rubber bands, but they could risk 25 and hope
for experimental error to be on their side.
Extensions: This project could be repeated using rubber bands with different strength coefficients
or other types of elastic materials. Dolls of differing weights can be used in discovering what effect
differing weights have on the rubber band. If weight is being considered, then use this to find the
stretch coefficient: Amount of stretch / weight = stretch factor.
PTE: Algebra Page 4
© 2003 Teachers Teaching With TechnologyBungee Barbie
Sample Solution
Problem: Develop a model to predict the number of rubber bands needed to drop an action figure from
a given height.
Assumptions:
1. The rubber bands are identical to one another.
2. Height and number of rubber bands are related linearly.
3. Barbie/Ken will start falling head first.
Procedure: Data is collected by measuring the height of Barbie’s fall with the number of rubber bands
varying from 1 to 6. Each trial is repeated three times and the results are averaged.
Data: Drop height in centimeters is listed below.
Number of Rubber Bands Trial 1 Trial 2 Trial 3 Average
1 31 33 30 31
2 52 55 51 53
3 72 74 75 73
4 93 92 94 93
5 116 115 120 117
6 133 137 140 137
Model: x = # of rubber bands; y = cliff height (cm)
Equation obtained by linear regression on TI-83 Plus/SE: y = 21.2 x + 9.8
Prediction: Given a test height of 595 cm, our model gives a prediction of 27.6 rubber bands. To be on
the safe side, we use 27 rubber bands. During the actual test we came within about 16centimeters of the
floor.
Reflection: One or two additional rubber bands could have been used to produce a safe jump. Possible
sources of error include consistency of rubber bands, linearity assumption at extreme heights when
rubber bands are stretched to a greater length, and the permanent deformation of bands after the first
jump. Fresh bands should always be used for data collection trials and the test jump.
PTE: Algebra Page 5
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