This preview shows pages 1–2. Sign up to view the full content.
Problem 1.15
[Difficulty: 5]
Given:
Data on sky diver:
M7
0
k
g
⋅
=
k
vert
0.25
Ns
2
⋅
m
2
⋅
=
k
horiz
0.05
2
⋅
m
2
⋅
=
U
0
70
m
s
⋅
=
Find:
Plot of trajectory.
Solution:
Use given data; integrate equation of motion by separating variables.
Treat the sky diver as a system; apply Newton's 2nd law in horizontal and vertical directions:
Vertical: Newton's 2nd law for the sky diver
(mass M) is (ignoring buoyancy effects):
M
dV
dt
⋅
Mg
⋅
k
vert
V
2
⋅
−
=
(1)
For
V
(
t
) we need to integrate (1) with respect to
t
:
Separating variables and integrating:
0
V
V
V
⋅
k
vert
V
2
−
⌠
⎮
⎮
⎮
⎮
⌡
d
0
t
t
1
⌠
⎮
⌡
d
=
so
t
1
2
M
k
vert
g
⋅
⋅
ln
⋅
k
vert
V
+
⋅
k
vert
V
−
⎛
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎠
⋅
=
Rearranging
o
r
Vt
()
⋅
k
vert
e
2
k
vert
g
⋅
M
⋅
t
⋅
1
−
⎛
⎜
⎝
⎞
⎠
e
2
k
vert
g
⋅
M
⋅
t
⋅
1
+
⎛
⎜
⎝
⎞
⎠
⋅
=
so
⋅
k
vert
tanh
k
vert
g
⋅
M
t
⋅
⎛
⎜
⎝
⎞
⎠
⋅
=
For
y
(
t
) we need to integrate again:
dy
dt
V
=
or
yt
V
⌠
⎮
⌡
d
=
0
t
t
⌠
⎮
⌡
d
=
0
t
t
⋅
k
vert
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '07
 Lear
 Fluid Mechanics

Click to edit the document details