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f
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o
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1
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s
5
f
t
1
k
t
5
k
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1
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2
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3
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4
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5
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1
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1
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m
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l
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84
1
5
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1
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2
a
1
fk
2
a
2
fk
2
F
1
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F
1
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1
a
1
; F
2
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2
a
2
.
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m
1
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2
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=
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1
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2
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1
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F
a
F
a
F
a
F
=
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2
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1,2
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0,64
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2
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Hl\_lF
2
G
43
4.
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m = 0,5
d]
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A
= 10 H
F
L
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F
C
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F =
F
A
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L
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C
⇒
F
A
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L
– F
C
= ma
⇒
⇒
a =
d]
0,5
H
2
H
5
H
10
−
−
=
−
−
m
F
F
F
C
L
A
fk
2
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F
2
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2
.
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l
F
U
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U
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2
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fk
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x
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G
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F
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F
1x
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F
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F
x
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x
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G
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F
1x
,
F
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, F
x
.
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1
x
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2x
G F
1x
GF
2x
=
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x
G
44
MijZ`g_gb_
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g
≈
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2
t = 2 c
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g
≈
fk
2
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2
2
gt
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2
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10
f
0,8
2
2
⋅
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g
h
= 0,4
k.
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Hl\_lt k
3.
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g
≈
fk
2
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f
t
1
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t = 1 c
J_r_gb_
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2
2
gt
⇒
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2
fk
10
f
45
2
2
⋅
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g
h
k
s
1
=
2
2
1
gt
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k
1
fk
10
2
2
⋅
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2
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(
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2
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2
2
2
t
t
g
gt
−
−
=
=
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(
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2
c
1
c
3
fk
10
2
k
3
fk
10
2
2
2
2
−
⋅
−
⋅
= 5
f
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1
, s
2
.
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1
fs
2
f
MijZ`g_gb_
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v
fk
v
1
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g
fk
2
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t
v
t
v
v
=
−
1
⇒
t =
2
fk
9,8
fk
9,8
=
g
v
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s =
2
2
gt
vt
−
fk
⋅
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( )
2
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k
fk
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2
2
⋅
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MijZ`g_gb_
1.
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1.
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g
≈
fk
2
m
1
d]
m
2
] d]
m
3
l d]
m
4
l d]
J_r_gb_
F
l
= mg
⇒
F
l
fk
2
⋅
d] G
F
l
fk
2
⋅
d] G
F
l
fk
2
⋅
d] G dG
F
l
fk
2
⋅
d]
⋅
10
5
G dG
GZclb F
l1
, F
l2
, F
l3
, F
l4
.
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2.
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g
≈
fk
2
; m
d]
J_r_gb_
F
l
= mg
d]
⋅
fk
2
G
GZclb
F
l
.
Hl\_l
F
l
G
3.
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g
≈
fk
2
;
F
l
G
J_r_gb_
F
l
= mg
⇒
m =
2
l
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KbeZ F
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2.
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46
MijZ`g_gb_
1.
>Zgh
r
kf f
v
fk
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Z =
r
v
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(
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f
21
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0
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20
2
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2
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2
.
2.
>Zgh
R
kf f
T
k
J_r_gb_
Z =
R
v
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T
R
T
l
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2
⇒
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T
R
2
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2
4
π
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2
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4
T
R
π
=
=
( )
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3
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.
GZclba.
Hl\_lZ
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10
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fk
2
.
3.
Z
1
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r
v
2
;
Z
2
=
r
v
r
v
2
2
2
2
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1
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ml\_j`^_gb_\_jgh
4.
>Zgh
T
1
k
T
2
k
J_r_gb_
(
)
.
4
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.
4
2
2
2
2
2
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1
2
2
1
2
1
1
T
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a
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R
T
R
R
v
a
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c
60
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3600
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2
2
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1
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1
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T
a
a
GZclb
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a
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Hl\_l
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5.
>Zgh
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10
24
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e
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22
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2
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10
8
f
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F
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2
e
a
r
F
F
G
= 6,67
⋅
10
-11
2
2
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f
G
⋅
×
2
8
22
24
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10
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10
7
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10
6
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⋅
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1,9
⋅
10
20
G
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p
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a
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F
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10
6
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10
9
,
1
24
20
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⋅
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3,17
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10
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2
;
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v =
r
a
p
=
f
10
84
,
3
fk
10
17
,
3
8
2
5
⋅
⋅
⋅
−
≈
fk
GZclbF
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,
Z
p
, v.
Hl\_lF
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1,9
⋅
10
20
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fk
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p
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10
-5
fk
2
.
47
MijZ`g_gb_
1.
>Zgh
h
df
⋅
10
6
f
F
a
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⋅
10
24
d]
R
a
= 6,4
⋅
10
6
f
G = 6,67
⋅
10
-11
2
2
d]
f
G
⋅
J_r_gb_
=
+
≈
h
R
M
G
v
a
a
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⋅
+
⋅
⋅
⋅
⋅
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=
−
f
10
6,4
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10
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10
6
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f
G
10
6,67
6
6
24
2
2
11
fk dfk
GZclbv.
Hl\_lv dfk
2.
>Zgh
v
dfk
⋅
10
3
fk
g
e
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fk
2
J_r_gb_
=
=
⇒
=
e
e
g
v
r
r
v
r
2
e
2
e
(
)
2
2
3
fk
1,6
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10
1,67
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⋅
10
6
f
⋅
10
3
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GZclb
r
e
.
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10
3
df
MijZ`g_gb_
1.
>Zgh
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x
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1
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v
2
dfq fk
m
l d]
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j = m
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48
2.
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1
l
m
2
l
v
2
fk
J_r_gb_
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m
1
v
1
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1
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2
1
2
1
v
m
m
m
+
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fk
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l
l
28
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+
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1.
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v
e
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m
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J_r_gb_
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e
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e
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e
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m
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t
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Q_j_ak L = 1/
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k
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f
T
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13,5
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270
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v
GZclb v.
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J_r_gb_
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MijZ`g_gb_
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47
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50
1
1
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=
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k
60
1
,
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c
J_r_gb_
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10
c
10
1
1
7
7
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T
GZclb
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.
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7
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10
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c
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10
8
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8
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10
8
fk
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10
5
f
600
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10
3
5
8
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⋅
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λ
c
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.
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5
=p
4.
AgZy kdhjhklv jZkijhkljZg_gby kb]gZeZ k hgZ jZ\gZ kdhjhklb
k\_lZ b \j_fy _]h jZkijhkljZg_gby t g_ljm^gh jZkkqblZlv
ijhc^_ggh_ jZkklhygb_ S AZ \j_fy t kb]gZe ijhc^_l jZkklhygb_ S
lm^Zb h[jZlghbke_^h\Zl_evghS = ct/2.
5.
G_la\mdh\u_\hegug_jZkijhkljZgy_lky\ \Zdmmf_
MijZ`g_gb_
1.
K
12
6
²Z_f Li
6
3
²Z_f Ca
40
20
²Z_f
2. 6, 3, 20.
55
3.
<
n =
Z_f
1
Z_f
6
jZa
4.
Z [ Z_f\ \ jZa] ^ _ `
5.
N
O
O
K
14
7
14
7
0
1
0
14
1
6
14
6
=
⇒
+
→
−
−
+
_
²Zahl
MijZ`g_gb_
H
O
He
N
1
1
17
8
4
2
14
7
+
→
+
Bf__f Ke_^h\Zl_evgh
aZdhgkhojZg_gbyaZjy^Z\uihegy_lky
MijZ`g_gb_
1.
< y^j_ ZlhfZ [_jbeeby Be
9
4
gmdehgh\ ² ijhlhgh\ ²
g_cljhgh\²N = A + Z = 9 – 4 = 5.
2.
D
39
19
Z Z [ N
p
= Z
\ Q \ we_f_glZjguo
we_dljbq_kdboaZjy^Zo ] N
e
= N
p
^ _ ` : a N =
A – Z =
± b m Z_f
3.
Qbkeh ijhlhgh\ khhl\_lkl\_ggh we_dljhgh\ \ Zlhf_ jZ\gh _]h
ihjy^dh\hfm ghf_jm \ lZ[ebp_ F_g^_e__\Z ke_^h\Zl_evgh Z
eblbc[ nlhj
MijZ`g_gb_
Wlb Zlhfu bf_xl h^bgZdh\u_ fZkku gh bo obfbq_kdb_ k\hckl\Z
jZaebqguWlhh[tykgy_lkyl_fqlhm gbojZagu_aZjy^h\u_qbkeZ
ZagZqblb dhebq_kl\hwe_dljhgh\
MijZ`g_gb_
1.
He
Th
U
4
2
234
90
238
92
+
→
.
2.
~
U
Pa
;
~
Pa
Th
0
0
0
1
234
92
234
91
0
0
0
1
234
91
234
90
+
+
→
+
+
→
−
−
e
e
Ke_^h\Zl_evgh \
j_amevlZl_^\mo
β
jZkiZ^h\
MijZ`g_gb_
Ld gmdehgu bf_xl fZkkm lh f_`^m gbfb ^_ckl\mxl kbeu
]jZ\blZpbhggh]hijbly`_gby
56
AZ^Zqbij_^eZ]Z_fu_^eyih\lhj_gby
b ijbqZkZonbabdb\ g_^_ex
1.
>ey\_dlhjZ a
U
bf__fZ [ Z
y
± ±\ _Z
y
| =
]
2
2
)
5
2
(
)
5
,
0
5
,
0
(
|
|
−
+
−
=
a
U
= 3.
>ey\_dlhjZ
b
U
bf__fZ [ b
y
± \ _b
y
_ ]
2
2
)
0
4
(
)
1
4
(
|
|
−
+
−
=
b
U
= 5.
>ey\_dlhjZ
c
U
bf__fZ [ c
y
± \ _c
y
_ ]
2
2
)
1
1
(
)
4
6
(
|
|
−
−
−
=
c
U
= 2.
>ey\_dlhjZ
d
U
bf__fZ ± [ d
y
±± ±\ _d
y
_ ]
2
2
)
0
4
(
)
6
3
(
|
|
−
−
+
−
=
d
U
= 5
>ey\_dlhjZ
→
e
bf__fZ ± [ e
y
±± ± \
|e
y
_ ]
2
2
))
4
(
1
(
)
5
,
0
5
,
0
(
|
|
−
−
−
+
−
=
e
U
= 3.
2. a
x
= 0, b
x
=
|
|
b
U
, c
x
= 0, d
x
=
|
|
d
U
−
.
3.
Z A (0;2), B ± [ s
x
= 12 – 0 = 12, s
y
±± ±\ _s
x
| = 12,
|
s
y
| = 5;
]
2
2
)
2
3
(
)
0
12
(
|
|
−
−
+
−
=
s
U
= 13.
4.
x
y
B
A
s
AB
=
2
2
))
2
(
3
(
))
8
(
4
(
−
−
+
−
−
LZddZdimlvg_fh`_lij_\ukblv
i_j_f_s_gby fh^mevdhlhjh]h_klvgZbf_gvr__jZkklhygb_f_`^m
gZqZevghcb dhg_qghclhqdZfbimlb lhhgfh`_l[ulveb[hjZ\_g
eb[h[hevr_i_j_f_s_gbyghgb \dh_fkemqZ_g_f_gvr__]h
5.
Ijyfhebg_cguf jZ\ghf_jguf ^\b`_gb_f gZau\Z_lky lZdh_
^\b`_gb_ ijb dhlhjhf aZ h^bgZdh\u_ ijhf_`mldb \j_f_gb l_eh
kh\_jrZ_l h^bgZdh\u_ i_j_f_s_gby \^hev g_dhlhjhc hkb lZd dZd
^\b`_gb_ ijyfhebg_cgh_ Ihwlhfm s
x
= v
x
t
]^_ v
x
² ihklhyggZy
57
\_ebqbgZ oZjZdl_jbamxsZy kdhjhklv i_j_f_s_gby Bkoh^y ba
mjZ\g_gbyo = o
0
+ s
x
ihemqbfx = x
0
+ v
x
t.
6.
>Zgh
v
x
fkx
0
f
J_r_gb_
x(
t) =
x
0
+ v
x
t
⇒
x(t) = 3 + 5t.
GZclbx(t).
Hl\_lx(t) = (3 + 5t f
7.
x
i
x
l
x
\
X
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