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Final Project
Suppose that you have been hired to design a bungee jump. The length of the bungee cord is
L
, and the
bungee jump platform is assumed to be at height,
h
= 0, with
h
increasing in the downward direction (
g
is positive and assumed to be 9.81 m/s
2
). Using numerical integration techniques, you will look at the
trajectory of a bungee jumper from the platform to the end of the cord extension.
Background:
The bungee jump consists of two phases: free fall and bungee extension.
1. Free Fall
During the free fall the jumper is only subjected to two forces: gravity,
F
g
=
mg
and drag,
F
d
=

C
d
v
2
. This makes the acceleration on the jumper
a
(
t
) =
1
m
X
F
=
g

C
d
m
v
2
where
C
d
is the coeﬃcient of drag, and
m
is the mass of the jumper. The free fall is active as long
as the distance traveled is less than the length of the cord (
h
≤
L
). Using numerical integration
(discussed in class), the velocity at time
t
new
can be updated as
v
new
=
v
old
+ Δ
ta
=
v
old
+ Δ
t
±
g

C
d
m
v
2
old
²
In addition, the height can be updated as
h
new
=
h
old
+ Δ
tv
new
The new velocity and position then become the old velocity and position for the next iteration.
2. Bungee Extension
The bungee cord is modeled as a spring force with a spring constant
k
. Accordingly, the additional
force added by the bungee is
F
s
=
k
Δ
x
where
x
=
h

L
is the distance traveled since the bungee
became active. This makes the new acceleration on the jumper
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 Spring '07
 Hayes

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