Barbie Bungee Jump

 Barbie and her friends have decided to go bungee jumping over Christmas vacation.  Barbie is quite a daredevil, so she wants the biggest thrill possible—she hopes to come as close as possible to the ground before springing back up into the air.  However, numerous reports of fatalities from improperly measured bungee cords have her nervous.  You have been assigned to a team to test bungee cords of different lengths.  Your tests will determine the length of bungee cord that Barbie should use for a jump that is both safe and thrilling.

 

 

 

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Chris makes initial measurements to determine how far Barbie will fall with 6 rubber bands.    
     

     
     

     

Project Description by J. Rohling
Picture Descriptions by K. Fly
Pictures by S. Hayden
 

 

  

 

 

 

 

 

 

How Did I Determine this Equation?

            I determined this equation by drawing a line through the scatter plot that best represented the slope and general placement of the points.  Then I found tow points on the line, (14, 180) and (10, 130).  After that, I subtracted 130 from 180 and 10 from 14.  By doing that I got 50/4 or 25/2.  With the slope and a point, I determined the y intercept by finding what b equaled.  Finally, I plugged the numbers into y intercept form and got y = 25/2x  + 5.  This is shown in math below.

(10, 130) (14, 180)

180 -130          50 = 25 m                                130 = 25(10)               125 + b           

  14 -  10          4         2                                               2(1)                     1

                                                                         130 = 125b     

                                                                       -125   -125      

y = 25/2x + 5                                                       5 =   b

 

 

Calculations for the Four Final Jumps

 For all of the following equations, I will be filling in the number of centimeters into y and calculating the number of rubber bands needed.

 Classroom Ceiling

287 = 25/2x + 5

-   5              -  5

282 = 25x

 ______2

25       25

  2         2

 22.56 = x

 22 rubber bands; otherwise, she would hit her head and die.

 

Tip of Tower on Golden Gate Bridge

22,700 = 25x + 5

                  2

-        5           - 5

22,695 =  25x

_________2

25             25

  2               2

1815.6 = x

1,815 rubber bands

 

Eiffel Tower

30,050 = 25x + 5

                  2

        -5            -5

30,045 = 25x

                  2

        25    25

          2      2

 

2,403.6 = x          

 

2,403 rubber bands

 

BellSouth Building

 

18,800 = 25x + 5

                  2

        -5           - 5

18,795 = 25x

                  2

       25     25

         2       2

 

1,503.6 = x

 

1,503 rubber bands

 

Sears Tower

 44,200 = 25x + 5

                 2

       -5            -5

44,195 = 25x

                  2

       25     25

         2       2

 

3,535.6 = x

 3,535 rubber bands