Lecture 21
●
MEEN 357 Homework Solution
1
Lecture21HomeworkSolution2009.doc
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1.
A crazy man jumps out of an airplane over Aggieland.
In the coordinate system
fixed to the airplane, the ordinary differential equations governing his decent are
22
2
2
d
d x
dx
dx
dy
mc
dt
dt
dt
dt
⎛⎞⎛⎞
=−
+
⎜⎟⎜⎟
⎝⎠⎝⎠
(21.1)
and
2
2
d
d y
dy
dx
dy
m
g
dt
dt
dt
dt
+
−
(21.2)
where
80 kg
m
=
is the mass,
5.38 Nsec /m
d
c
=
is the drag coefficient and
2
9.81 m/sec
g
=
is the gravitational constant.
If the man jumps with an initial
horizontal velocity of 130 m/sec and an initial vertical velocity of 0 from an
initial height of 0 in his coordinate system, plot the trajectory
, i.e., his
x
and
y
positions, of the man for 5 seconds.
Solution:
The first step is to write the two coupled second order ordinary differential equations
(21.1) and (21.2) in normal form.
As with our many examples, you define the column
vector
x
by
1
2
3
4
x
x
dx
x
dt
x
y
x
dy
dt
⎡
⎤
⎢
⎥
⎡⎤
⎢
⎥
⎢⎥
⎢
⎥
==
⎢
⎥
⎢
⎥
⎢
⎥
⎣⎦
⎢
⎥
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 Fall '07
 ANAMALAI
 dt, dt dt, van der Pol

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