Graphics Programs Reference
In-Depth Information
19.
y
v
0
θ
x
t
= 0
8000 m
t
= 10 s
Aprojectile of mass
m
in free flight experiences the aerodynamic drag force
F
D
=
cv
2
, where
v
is the velocity. The resulting equationsofmotionare
c
m
v x
c
m
v y
x
=−
y
=−
−
g
x
2
y
2
v
=
+
If the projectile hits a target 8 km away aftera10sflight, determine the launch
velocity
v
0
and its angle of inclination
10
−
4
θ
. Use
m
=
20kg,
c
=
3
.
2
×
kg/m and
g
=
9
.
80665 m/s
2
.
20.
w
0
N
N
x
L
v
The simply supportedbeam carries a uniform load of intensity
w
0
and the tensile
force
N
. The differentialequation for the vertical displacement
v
can be shown
to be
d
4
v
dx
4
d
2
v
dx
2
N
E I
w
0
E I
−
=
d
2
v
dx
2
where
E I
is the bending rigidity. The boundary conditions are
v
=
/
=
0
x
L
and
y
E I
w
0
L
4
v
transforms
at
x
=
0 and
x
=
L
.Changing the variables to
ξ
=
=
the problem to the dimensionless form
d
4
y
d
d
2
y
d
NL
2
E I
−
β
=
1
β
=
4
ξ
2
ξ
ξ
=
0
=
ξ
=
1
=
d
2
y
d
d
2
y
d
y
|
ξ
=
0
=
y
|
ξ
=
1
=
0
2
2
ξ
ξ
Determine the maximum displacement if(a)
β
=
1
.
65929 and (b)
β
=−
1
.
65929
(
N
iscompressive).
21.
Solve the boundary value problem
y
+
yy
=
y
(0)
0,
y
(
0
y
(0)
=
=
∞
)
=
2
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