19. IhkqblZ_fmkdhj_gb_ihnhjfme_
2
2
t
s
a = aZf_jb ijhc^_ggh_ l_e_`dhc jZkklhygb_ s b j_fy __
^b`_gbyt?kebmf_gvrblvkbem^_cklmxsmxgZl_e_`dm ^Z
jZaZ udexq_gb_f h^gh]h ba _glbeylhjh
118. xt = o0 + sto f f f
MijZ`g_gb_
1. =jZnbdfh^mey_dlhjZkdhjhklbg_fh`_lgZoh^blvkyih^hkvx
Otihkdhevdmfh^mev_dlhjZkdhjhklbk_]^Ziheh`bl_e_g=jZnbd
ijh_dpbb _dlhjZ kdhjhklb fh`_l gZoh^blvky ih^ hkvx Ot,
ihkdhevdm agZd aZbkbl ijh_dpbb _dlhjZ kdhjhklb hl u[hjZ
kbkl_fudhhj^bgZl
2.
80
60
–90
vx, dfq
tq
119. 40
MijZ`g_gb_
1. I_juc Zlhfh[bev ^b]Zeky k [hevrbf mkdhj_gb_f ihkdhevdm
_]hkdhjhklvaZh^bgZdhu_ijhf_`mldbj_f_gbhajZklZeZ[uklj__
2.
Zgh
t = 30 c
v1 fk
v2 fk
J_r_gb_
.fk5,1
k30
fk10fk55 212
=
−
=
−
=
t
vv
a
GZclbZ. Hl_la fk2
.
3.
Zgh
t = 12 c
v2 – v1 fk
J_r_gb_
.fk5,0
k12
fk6 212
==
−
=
t
vv
a
GZclbZ. Hl_la fk2
.
MijZ`g_gb_
1.
Zgh
v1 fk
t = 4 c
a = –20 fk2
J_r_gb_
t
vv
a 12 −
= ⇒ v2 = v1 + at =
fk ±fk2
) ⋅ k fk
GZclb v2. Hl_lv2 fk
2.
Zgh
a fk2
v1 = 0
v2 fk
J_r_gb_
k10
fk0,2
fk2
2
2212
===⇒=
−
=
a
v
t
t
v
t
vv
a
GZclbt. Hl_lt k
3.
Y[
W
120. 41
4.
vx
t5 10
5
-5
5. eyl_eZ,Z fk2
^eyl_eZ,,Z fk2
.
MijZ`g_gb_
1.
Zgh
t = 5 c
Zo fk2
v0o dfq fk
J_r_gb_
sx =
2
2
0
ta
tv x
o + fk ⋅ k
( )
2
k5fk0,5
22
⋅
=
f
GZclbsx. Hl_lsx f
2.
Zgh
t = 20 c
Zo fk2
v0o fk
J_r_gb_
sx =
2
2
0
ta
tv x
o + ; ao =
t
v x0
− ⇒ sx =
t
tv
tv x
o
2
2
0
0 − =
2
0 tv x
=
fk ⋅ k f
GZclbsx. Hl_lsx f
MijZ`g_gb_
1.
Zgh
s3 f
t1 k
J_r_gb_
s1 : s2 : s3 = 1 : 3 : 5; s1 : 2 f = 1 : 5 ⇒ s1 = 5f2 = 0,4 f;
s1 =
2
2
1at
⇒ a = 2
1
12
t
s
=
( )2
k1
f0,42⋅
= 0,8 f/k2
.
GZclb s1, a. Hl_ls1 fa fk2
.
2.
Zgh
s5 f
t1 k
t5 k
J_r_gb_
s1 : s2 : s3 : s4 : s5 = 1 : 3 : 5 : 7 : 9; s1 : 6,3 f = 1 : 9 ⇒
⇒ s1 = 5f6,3 = 0,7 f;
s1 =
2
2
1at
⇒ a = 2
1
12
t
s
=
( )2
k1
f0,72⋅
= 1,4 f/k2
;
v5 = at5 fk2
⋅ k fk
GZclbv5. Hl_lv5 fk
121. 42
MijZ`g_gb_
1. fk
2. G_l ihkdhevdm b ^_j_h b hdaZe `_kldh kyaZgu k ^jm]hc
kbkl_fhchlkq_lZ²A_fe_c
3. Ijbmkehbbg_ih^b`ghklbwlbol_ehlghkbl_evgh^jm]^jm]Z
4. dfq fk
5*.
Zgh
v1 dfq fk
v2 fk
J_r_gb_
v = v1 + v2 fk fk fk
va = v2 – v1 fk ±fk fk
GZclbv, va. Hl_lv fkva fk
MijZ`g_gb_
AZdhgbg_jpbbuihegy_lky kbkl_f_hlkq_lZkyaZgghck A_fe_cb
kbkl_f_ hlkq_lZ kyaZgghc k ih_a^hf h j_fy _]h
ijyfhebg_cgh]h b jZghf_jgh]h ^b`_gby g_ uihegy_lky
kbkl_f_ hlkq_lZ kyaZgghc k ih_a^hf h j_fy _]h lhjfh`_gby
Bg_jpbZevghckbkl_fhcfh`ghkqblZlva_fexZ ih_a^²g_evay
MijZ`g_gb_
1.
Zgh
Z fk2
m d]
J_r_gb_
IhhfmaZdhgmGvxlhgZ
F = ma d]⋅ fk2
G
GZclbF. Hl_lF G
2.
Zgh
t = 20 c
v fk
m l ⋅105
d]
J_r_gb_
F = ma ²hcaZdhgGvxlhgZ
a =
t
v
⇒ F =
t
mv
=
k20
fk4d]10841 5
⋅⋅,
=
G dG
GZclbF. Hl_lF dG
3.
Zgh
m1 = m2
a1 fk2
a2 fk2
F1 = 1,2 H
J_r_gb_
IhhfmaZdhgmGvxlhgZ
F1 = m1a1; F2 = m2a2. Ldm1 = m2lhihemqZ_f
==⇒=
1
12
2
2
2
1
1
a
Fa
F
a
F
a
F
=
⋅
2
2
fk0,08
G1,2fk0,64
9,6 H.
GZclbF2. Hl_lF2 G
122. 43
4.
Zgh
m = 0,5 d]
FA = 10 H
FL = 5 H
FC = 2 H
J_r_gb_
IhhfmaZdhgmGvxlhgZF = ma.
F = FA – FL – FC ⇒ FA – FL – FC = ma ⇒
⇒a =
d]0,5
H2H5H10 −−
=
−−
m
FFF CLA
fk2
.
GZclbF2. Hl_la fk2
.
5. Ijb ^b`_gbb _jo kdhjhklv b i_j_f_s_gb_ ijhlbhiheh`gh
gZijZe_gu k kbehc ly`_klb mkdhj_gb_ ² khgZijZe_gh Ijb
^b`_gbbgbakdhjhklvi_j_f_s_gb_b mkdhj_gb_khgZijZe_guk
kbehcly`_klb
6. Mkdhj_gb_ k_]^Z khgZijZe_gh k jZgh^_cklmxs_c
ijbeh`_gguod l_emkbeKdhjhklvb i_j_f_s_gb_fh]ml[ulvdZd
khgZijZe_guk jZgh^_cklmxs_cijbeh`_gguod l_emkbelZdb
ijhlbhiheh`ghgZijZe_gu
MijZ`g_gb_
1. GZ l_eh ^_cklmxl kbeZ ly`_klb lF
7
b kbeZ j_Zdpbb hihju N
7
kfjbk
133. 44
MijZ`g_gb_
1.
Zgh
g ≈ fk2
t = 2 c
J_r_gb_
h =
2
2
gt
=
( )
2
k2fk10
22
⋅
f
GZclbh. Hl_lh f
2.
Zgh
g ≈ fk2
h = 80 cf f
J_r_gb_
h =
2
2
gt
⇒ t = 2
fk10
f0,822 ⋅
=
g
h
= 0,4 k.
GZclbt. Hl_lt k
3.
Zgh
g ≈ fk2
h = 45 f
t1 = 1 c
∆t = 1 c
J_r_gb_
h =
2
2
gt
⇒ t = 2
fk10
f4522 ⋅
=
g
h
k
s1 =
2
2
1gt
=
( )
2
k1fk10
22
⋅
= 5 f;
s2 =
( )
2
û
2
22
ttggt −
− =
=
( ) ( )
2
c1c3fk10
2
k3fk10
2222
−⋅
−
⋅
= 5 f
GZclb t, s1, s2. Hl_lt ks1 fs2 f
MijZ`g_gb_
Zgh
v fk
v1 = 0
g fk2
J_r_gb_
g =
t
v
t
vv
=
− 1
⇒ t = 2
fk9,8
fk9,8
=
g
v
=1 c;
s =
2
2
gt
vt − fk ⋅ k ±
( )
2
1kfk9,8
22
⋅
f
GZclbt, s. Hl_lt ks f
MijZ`g_gb_
1. k_l_eZiZ^ZxlgZa_fexih^^_cklb_fkbeuly`_klb
2. KlZgpby m^Zey_lky hl A_feb ijb[eb`Zykv d Emg_ BaaZ
baf_g_gbc jZkklhygbc f_`^m ieZg_lZfb b klZgpb_c kbeZ __
ijbly`_gby d A_fe_ mf_gvrZ_lky Z kbeZ ijbly`_gby d Emg_
139. 46
MijZ`g_gb_
1.
Zgh
r kf f
v fk
J_r_gb_
Z =
r
v2
=
( )
f21,0
fk20
2
≈ fk2
.
GZclba. Hl_lZ ≈ fk2
.
2.
Zgh
R kf f
T k
J_r_gb_
Z =
R
v2
; v =
T
R
T
l π
=
2
⇒ Z =
RT
R
2
22
4π
= 2
2
4
T
Rπ
=
=
( )
( )2
2
k60
f02,014,34 ⋅⋅
≈ 2⋅10-4
fk2
.
GZclba. Hl_lZ ≈ 2⋅10-4
fk2
.
3. Z1 =
r
v2
; Z2 =
r
v
r
v 22
2
2/
⋅= = 2a1 ⇒ ml_j`^_gb__jgh
4.
Zgh
T1 k
T2 k
J_r_gb_
( ) .
4
:gZeh]bqgh.
42
2
2
2
22
1
22
1
2
1
1
T
R
a
T
R
R
TR
R
v
a
π
=
π
=
π
==
.3600
c60
c3600
vghKe_^hZl_e
22
2
1
2
1
=
=
=
T
T
a
a
GZclb
2
1
a
a
. Hl_l
2
1
a
a
= 3600.
5.
Zgh
Fa = 6⋅1024
d]
Fe = 6⋅1022
d]
G=6,67⋅10-11
2
2
d]
fG⋅
r = df
= 3,84⋅108
f
J_r_gb_
Z
145. 106,4f10(2,6
d]106
d]
fG
106,67 66
24
2
2
11
fk dfk
GZclbv. Hl_lv dfk
2.
Zgh
v dfk ⋅103
fk
ge ≈ fk2
J_r_gb_
==⇒=
e
e
g
v
r
r
v
r
2
e
2
e
( )
2
23
fk1,6
fk101,67⋅
=
= 1,7⋅106
f ⋅103
df
GZclb re. Hl_lre = 1,7⋅103
df
MijZ`g_gb_
1.
Zgh
v1x = –v2x fk
m = 0,2 d]
J_r_gb_
p1x = mv1x d]⋅ fk d]⋅fk
p2x = – p1x ±d]⋅fk
_dlhjubfimevkhfZrbgg_jZguldhgb
ijhlbhiheh`gh gZijZe_gu Fh^meb
_dlhjhbfimevkhjZgu
GZclb p1x, p2x. Hl_lp1x d]⋅fkp2x ±d]⋅fk
2.
Zgh
v1 dfq fk
v2 dfq fk
m l d]
J_r_gb_
∆j = m∆v = m(v2 – v1) =
d]⋅ fk ± fk
147. 48
2.
Zgh
m1 l
m2 l
v2 fk
J_r_gb_
AZibr_faZdhgkhojZg_gbybfimevkZ
m1v1 = (m1 + m2)v2 ⇒ v1 = 2
1
21
v
m
mm +
=
= fk0,5
35l
l28l35
⋅
+
fk
GZclb v1. Hl_lv1 fk
MijZ`g_gb_
1.
Zgh
ve fk
m d]
v fk
me d]
J_r_gb_
AZibr_faZdhgkhojZg_gbybfimevkZ
(me + m)ve + mv = mev ⇒ v =
e
ee )(
m
vmvmm ++
=
=
( )
d]200
fk8d]5fk2d]5d]200 ⋅+⋅+
fk
GZclb v. Hl_lv fk
2.
Zgh
mj ] d]
mi ] d]
vi fk
J_r_gb_
AZibr_faZdhgkhojZg_gbybfimevkZ
mjvj=mivi⇒vj=
j
ii
m
vm
= ≈
⋅
d]0,3
fk100d]0,1
fk
GZclb vj. Hl_lvj ≈ fk
MijZ`g_gb_
1. Dhe_[Zl_evgufb kbkl_fZfb yeyxlky [ ] _ G_ yeyxlky
dhe_[Zl_evgufbZ^
2. Z
151. ^Zyey_lky
MijZ`g_gb_
1. :fieblm^Z : qZklhlZ ν i_jbh^ L ² ihklhyggu_ F, v —
i_j_f_ggu_
2.
Zgh
ν = =p
J_r_gb_
T = k5,0
=p2
11
==
ν
GZclb T. Hl_lT k
152. 49
3.
Zgh
T k
J_r_gb_
ν = =p2
c5,0
11
==
T
GZclb ν. Hl_lν =p
4.
Zgh
n = 600
t fbg k
J_r_gb_
ν = ;
1
T
=p10
c60
600
===ν⇒=
t
n
n
t
T
GZclb ν. Hl_lν =p
5. kfkfkfkf
6.
Zgh
A = 10 kf
ν = 0,5 =p
t k
J_r_gb_
T =
=p5,0
11
=
ν
= 2 c AZ k l_eh kh_jrZ_l ihegh_
dhe_[Zgb_b ijhc^_limlvS = 4: kf
GZclb S. Hl_lS kf
7. Dhe_[exlky h^bgZdhuonZaZo kemqZyo[
170. MijZ`g_gb_
1.
Zgh
λ f
T k
J_r_gb_
fk20
k13,5
f270
==
λ
=
T
v
GZclb v. Hl_lv fk
2.
Zgh
ν =p
v fk
J_r_gb_
f7,1
=p200
fk340
==
ν
=λ
v
GZclb λ. Hl_lλ f
3.
2.
Zgh
v fk
λ f
J_r_gb_
k4
fk1,5
f6
==
λ
=
T
v
GZclbT. Hl_lT = 4 c.
MijZ`g_gb_
E_lysZyilbpZkha^Z_lbgnjZamdhu_hegu
MijZ`g_gb_
1. DhfZjAmdkha^ZZ_fucbfkZfucukhdbc
2. Mf_gvrblkyihkdhevdmqZklhlZ__ jZs_gbylZd`_mf_gvrblky
3. Ijb ihur_gbb l_fi_jZlmju kljmgZ jZkly]bZ_lky i_jbh^ __
dhe_[Zgbc m_ebqbZ_lky qZklhlZ b khhl_lkl_ggh ukhlZ
amqZgbymf_gvrZ_lky
MijZ`g_gb_
1. G_lf_`^mA_fe_cb Emghcg_lmijm]hckj_^uihdhlhjhcfh`_l
jZkijhkljZgylvkyamd
2. Amdhu_hegujZkijhkljZgyxlkyihgblb
171. 51
MijZ`g_gb_
1.
Zgh
λ f
T k
J_r_gb_
fk1450
k0,002
f9,2
==
λ
=
T
v
GZclb v. Hl_lv fk
2.
Zgh
v1 fk
v2 fk
v3 fk
ν =p
J_r_gb_
;f47,0
=p725
fk3401
1 ≈=
ν
=λ
v
;f05,2
=p725
fk14832
2 ≈=
ν
=λ
v
.f59,7
=p725
fk55003
3 ≈=
ν
=λ
v
GZclbλ1,λ2,λ3. Hl_lλ1 ≈ fλ2 ≈ fλ3 ≈ f
3. Amd [m^_l jZkijhkljZgylvky b ih f_lZeem b ih ha^mom b
q_eh_dmkeurbl^Zm^ZjZ
4.
Zgh
ta k
va fk
tiZj k
Sa = SiZj
J_r_gb_
Sa = vata; SiZj = viZjtiZj; Sa = SiZj; vata = viZjtiZj ⇒
⇒ fk20
k34
k2fk340
iZj
aa
iZj =
⋅
==
t
tv
v
GZclbviZj. Hl_lviZj fk
5. Dh]^Zb^bfu_b keurbfu_m^ZjugZqbgZxlkhiZ^ZlvkghZlh
wlhagZqblqlhq_eh_dkeurblij_^u^msbci_j_^b^bfufm^Zj
MijZ`g_gb_
1. Kms_klm_l
2. FZ]gblgh_ ihe_ [m^_l ^_cklhZlv gZ klj_edm k gZb[hevr_c
kbehc lhqd_ N k gZbf_gvr_c ² lhqd_ F K jZkklhygb_f
fZ]gblgh_ihe_hkeZ[_Z_l
MijZ`g_gb_
1. Z
173. lhqd_:.
2.
GZ iZju lhq_d P − Q, X − Y kh
klhjhgu g_h^ghjh^gh]h fZ]gblgh]h
ihey ^_cklmxl kbeu h^bgZdhu_
dZd ih fh^mex lZd b ih
gZijZe_gbx ld PO = QO, XO =
YO.
,
,
;
3
4
2
174. 52
MijZ`g_gb_
1.
2.
3. K__jguc ihexk gZoh^blky kijZZ Z x`guc ke_Z Bo
iheh`_gb_fh`ghbaf_gblvihf_gyiheyjghklvkhe_ghb^Z
4. Lhd[m^_ll_qvhllhqdbS d lhqd_N.
5. KijZZ²k__jgucihexkke_Z±x`gucihijZbem ijZhc
jmdb
175. 6. i_jhf kemqZ_ aZbfh^_cklb_ h[mkehe_gh fZ]gblgufb
kbeZfbhlhjhf±dmehghkdbfb
MijZ`g_gb_
1. IhijZbeme_hcjmdbhij_^_ey_fqlhijZh
2. IhijZbem e_hcjmdbhij_^_ey_fqlhlhdl_q_lhllhqdbB d
lhqd_ A b ke_^hZl_evgh _jogbc ihexk bklhqgbdZ lhdZ
ih^dexq_g d hljbpZl_evghfm ihexkm Z gb`gbc ² d
iheh`bl_evghfm
176. 53
3. GZ e_hf jbkmgd_ e_uc ijhh^gbd ^b`_lky _jo ijZuc
ijhh^gbd²gbaGZijZhfjbkmgd_e_ucijhh^gbd^b`_lky
gbaijZucijhh^gbd²_jo
4.
v
7
F
7
5. Ih ijZbem e_hc jmdb hij_^_ey_f qlh wlh iheh`bl_evgh
aZjy`_ggZyqZklbpZ
MijZ`g_gb_
1.
Zgh
I = 4 A; F = 0,2 H
l kf f
J_r_gb_
Le5,0
:4f0,1
G2,0
=
⋅
==
Il
F
B
GZclbB. Hl_lB Le
2. FZ]gblgZy bg^mdpby g_ baf_gy_lky hgZ ihklhyggZy _ebqbgZ
Baf_gy_lkylhevdhkbeZ^_cklmxsZygZijhh^gbd²hgZlZd`_
dZdb lhdmf_gvrZ_lky jZaZ
MijZ`g_gb_
FZ]gblguc ihlhd ijhgbauZxsbc dZlmrdm D2 fh`gh f_gylv
iml_fbaf_g_gbyaZbfghchjb_glZpbbdZlmr_db baf_g_gb_fkbeu
lhdZj_hklZlhfR bebaZfudZgb_fjZafudZgb_fdexqZD
MijZ`g_gb_
1. Baf_gblvfZ]gblgucihlhdq_j_adZlmrdmD2 iml_fhibkZgguf
mijZ`g_gbb
2. Bg^mdpbhgguclhdhagbdZ_l kemqZ_]
231. 22
)23()012(|| −−+−=s
7
= 13.
4.
x
y
B
A
sAB = 22
))2(3())8(4( −−+−− LZddZdimlvg_fh`_lij_ukblv
i_j_f_s_gbyfh^mevdhlhjh]h_klvgZbf_gvr__jZkklhygb_f_`^m
gZqZevghcb dhg_qghclhqdZfbimlb