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2. 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MijZ`g_gb_........................... 39 MijZ`g_gb_........................... 39 MijZ`g_gb_........................... 39 MijZ`g_gb_........................... 39 MijZ`g_gb_........................... 40 MijZ`g_gb_........................... 40 MijZ`g_gb_........................... 41 MijZ`g_gb_........................... 41 MijZ`g_gb_.......................... 42 MijZ`g_gb_.......................... 42 MijZ`g_gb_.......................... 42 MijZ`g_gb_.......................... 43 MijZ`g_gb_.......................... 44 444 5. MijZ`g_gb_..........................MijZ`g_gb_..........................44MijZ`g_gb_..........................45MijZ`g_gb_..........................45MijZ`g_gb_..........................46MijZ`g_gb_..........................47MijZ`g_gb_..........................47MijZ`g_gb_..........................47MijZ`g_gb_..........................48MijZ`g_gb_..........................48MijZ`g_gb_..........................48MijZ`g_gb_..........................49MijZ`g_gb_..........................49MijZ`g_gb_..........................50MijZ`g_gb_..........................50MijZ`g_gb_..........................50MijZ`g_gb_..........................50MijZ`g_gb_..........................50MijZ`g_gb_..........................51MijZ`g_gb_..........................51MijZ`g_gb_..........................51MijZ`g_gb_..........................52MijZ`g_gb_..........................52MijZ`g_gb_..........................53MijZ`g_gb_..........................53MijZ`g_gb_..........................53MijZ`g_gb_..........................53MijZ`g_gb_..........................54MijZ`g_gb_..........................5454 5 6. MijZ`g_gb_.......................... MijZ`g_gb_.......................... 55 MijZ`g_gb_.......................... 55 MijZ`g_gb_.......................... 55 MijZ`g_gb_.......................... 55 55AZ^Zqbij_^eZ]Z_fu_ ^eyihlhj_gby bijb qZkZo nbabdb g_^_ex .......... 56EZ[hjZlhjgu_ jZ[hlu .................. 64 EZ[hjZlhjgZy jZ[hlZ ................. EZ[hjZlhjgZy jZ[hlZ ................. 64 EZ[hjZlhjgZy jZ[hlZ ................. 67 EZ[hjZlhjgZy jZ[hlZ ................. 67 EZ[hjZlhjgZy jZ[hlZ ................. 68 EZ[hjZlhjgZy jZ[hlZ ................. 69 706 7. hijhku1.1. FZl_jbZevgZy lhqdZ h[eZ^Z_l fZkkhc gh bf__l ij_g_[j_`bfhfZeu_jZaf_ju2. FZl_jbZevgZylhqdZ wlhZ[kljZdlgh_ihgylb_3. eymijhs_gbyaZ^Zq4. Dh]^Z mkehbbaZ^ZqbjZaf_jZfbwlh]hl_eZfh`ghij_g_[j_qv5. AZ fZl_jbZevgmx lhqdm fh`gh ijbgylv Zlhfh[bev ijbhij_^_e_gbb _]h kdhjhklb gZ fZjrjml_ ] Ijhlbgh ] FhkdZWlhl `_ Zlhfh[bev g_evay kqblZlv fZl_jbZevghc lhqdhc ijbjZkq_l_^Ze_gbyhdZauZ_fh]hbfgZ^hjh]m6. IjbihklmiZl_evghf^b`_gbb7. FZl_jbZevghc lhqdhc gZauZ_lky l_eh jZaf_jZfb dhlhjh]hfh`ghij_g_[j_qv mkehbyo^ZgghcaZ^Zqb8. Ijbijyfhebg_cghf^b`_gbbl_eZ9. Kbkl_fZhlkq_lZhlghkbl_evghdhlhjhcjZkkfZljbZxl^b`_gb_ij_^klZey_l kh[hc khhdmighklv kbkl_fu dhhj^bgZl ijb[hjZ ^eybaf_j_gby j_f_gb b lhqdb hlkq_lZ k dhlhjhc kyaZgZ kbkl_fZdhhj^bgZl2.1. G_lk_aZbkblhlljZ_dlhjbb^b`_gbyG_evaymagZlv]^_[m^_lZlhfh[bevq_j_a qZk_kebg_agZ_rvihdZdbf^hjh]Zfhgih_^_l2. _dlhjgZijZe_gguchllhqdbhlkq_lZgZqZeZ^b`_gbyd lhqd_hlkq_lZdhgpZ^b`_gbyl_eZ3. Fh`gh3.1. uqbke_gbyijhbah^ylkhkdZeyjgufb_ebqbgZfb2. ?keb _dlhj khgZijZe_g k hkvx lh _]h ijh_dpby gZ g__ [m^_liheh`bl_evgZ b gZh[hjhl _keb _dlhj ijhlbhiheh`gh gZijZe_ghkblh_]hijh_dpbygZg__[m^_lhljbpZl_evgZ3. o1 = o0 + so.4.1. Kdhjhklvx jZghf_jgh]h ijyfhebg_cgh]h ^b`_gby gZauZ_lky7;ihklhygguc _dlhj vjZguc hlghr_gbx i_j_f_s_gby s l_eZ aZ ; 7 sex[hcijhf_`mlhdj_f_gbt d agZq_gbxwlh]hijhf_`mldZ v = . t7 8. 2. Ihnhjfme_sx = vxt.3. Ijbijyfhebg_cghfjZghf_jghf^b`_gbb4. Wlhb^ghbajbkmq_[gbdZ5. Hgb^b`mlkyjZghf_jgh jZaguogZijZe_gbyokhkdhjhklyfbjZgufbihfh^mex b dfq 5.1. D g_jZghf_jghfm^b`_gbx2. Kdhjhklvl_eZ ^Zgghclhqd_ ^Zggucfhf_glj_f_gb 73. Mkdhj_gb_f jZghmkdhj_ggh]h ^b`_gby l_eZ a gZauZ_lky 7_ebqbgZjZgZyhlghr_gbxbaf_g_gbykdhjhklb v d ijhf_`mldm 7 7 77 v v v 0j_f_gbtaZdhlhjucwlhbaf_g_gb_ijhbahreh a = =.4. b`_gb_k ihklhyggufmkdhj_gb_f tt5. HgihdZauZ_l[ukljhlmbaf_g_gbyfh^mey_dlhjZkdhjhklb6.kbkl_f_KBfk2.7. M_ebqbZ_lky ijb iheh`bl_evghf mkdhj_gbbwlhf kemqZ__dlhjkdhjhklbb _dlhjmkdhj_gbykhgZijZe_gu 9. mf_gvrZ_lkyijb hljbpZl_evghfwlhf kemqZ_ _dlhj kdhjhklb b _dlhjmkdhj_gbyijhlbhiheh`ghgZijZe_gu 10. 6.1. Z 11. vx = v0x + axt[ 12. vx = axt.2.h[hbokemqZyoijyfZy kemqZ_ Zijhoh^ysZyq_j_agZqZehkbkl_fudhhj^bgZl3. Wlb ^b`_gby jZghmkdhj_ggu_ h^gZdhi_jhf kemqZ_mkdhj_gb_iheh`bl_evghZ hlhjhfhljbpZl_evgh 7.1. Ijh_dpby_dlhjZi_j_f_s_gbyuqbkey_lkyihnhjfme_ axt 2 s x = v0 x t + .Ih^klZbf wlmnhjfmemujZ`_gb_^eyijh_dpbbmkdhj_gby 2 v v0 xax = x.Ihemqbf tv v0 x t 2 v0 x + v xs x = v0 x t + x = t . t 22 8 13. LZddZdv0x = AO, vx = BC, t = OB kfjbkZ 14. mq_[gbdZ 15. lhfuihemqZ_fqlhijh_dpby_dlhjZi_j_f_s_gby s x = AO + BC OBjZgZiehsZ^bnb]mjuOACB ijyfhm]hevghcljZi_pbbk2hkghZgbyfbAO, BC b ukhlhcOB.axt 22. s x = v0 x t + . 2 8.1. Ihnhjfme_ s x =^eyijh_dpbbi_j_f_s_gby s = 2 axt at 2^eyfh^mey_dlhjZi_j_f_s_gby 222.n2 jZaihkdhevdms ~ t2 s n a (nt1 ) 2 / 23. =2= n2 . st14. DZdjy^ihke_^hZl_evguog_q_lguoqbk_eat1 / 25. eyhij_^_e_gbyjZghmkdhj_ggh]h^b`_gby1.jZaguokbkl_fZohlq_lZwlb_ebqbgubf_xljZagu_agZq_gbyb 9.ihjZaghfmhjb_glbjhZggu2. RZjbd iZ^Zxsbc gZ ihe ^b`ms_]hky Zlhfh[bey g_ bf__l]hjbahglZevghc kdhjhklb hlghkbl_evgh g_]h Hlghkbl_evgh A_febhgbf__lkdhjhklvjZgmxkdhjhklbZlhfh[bey3. Kdhjhklv imlv ljZ_dlhjby b l^ jZaebqgujZaguo kbkl_fZohlkq_lZ4. =_ebhp_gljbq_kdZy kbkl_fZ kyaZgZ k Khegp_f ]_hp_gljbq_kdZyk A_fe_c5. Kf_gZ^gyb ghqbh[tykgy_lkyjZs_gb_fA_febhdjm]kh_chkb1. JZghf_jghb ijyfhebg_cghbebihdhblky 10.2. G_l3. L_hjby :jbklhl_ey aZdexqZxsZykylhf qlh ijb hlkmlklbbg_rg_]hha^_cklbyl_ehfh`_llhevdhihdhblvky4. L_f qlh ih =Zebe_x l_eZ fh]ml jZghf_jgh ^b]Zlvky hlkmlklbbg_rgbokbe5. Hiul bah[jZ`_gguc gZ jbkmq_[gbdZ ^hdZauZ_l lh qlhihfbfh bg_jpbZevguo kbkl_f hlkq_lZdhlhjuo uihegy_lkyi_juc aZdhg GvxlhgZ 16. kms_klmxl kbkl_fu bgh]h oZjZdl_jZ Hg 9 17. khklhblke_^mxs_f GZ l_e_`d_ h^bg rZjbd e_`bl gZ]hjbahglZevghc ih_joghklb Z lhjhc ih^_rbZ_lky gZ gblbKgZqZeZ l_e_`dZ ^b`_lky ijyfhebg_cgh b jZghf_jgh bwlhfkemqZ_ h[Z rZjbdZ gZoh^ylkyihdh_ hlghkbl_evgh l_e_`db Klhbllhevdh ijb^Zlv l_e_`d_ mkdhj_gb_ eb[h __ ijblhjfhablv eb[hih^lhedgmlv 18. dZd rZjbdb ijb^ml^b`_gb_ k mkdhj_gb_fhlghkbl_evghl_e_`dbLZdbfh[jZahfhlghkbl_evghl_e_`dbi_jucaZdhgGvxlhgZg_uihegy_lky6. Kms_klmxl kbkl_fu hlkq_lZ hlghkbl_evgh dhlhjuo l_eZkhojZgyxl khx kdhjhklv g_baf_gghc _keb gZ gbo g_ ^_cklmxlg_rgb_ kbeu beb bo ^_cklb_ kdhfi_gkbjhZgh LZdb_ kbkl_fugZauZxlkybg_jpbZevgufb7. Bg_jpbZevgu_kbkl_fum^he_lhjyxli_jhfmaZdhgmGvxlhgZg_bg_jpbZevgu_g_l8. Fh`gh9. G_l 11.1. Ijbeh`_ggZyd l_emkbeZ2. Q_f [hevr_ fhsghklv Zlhfh[bey Z khhl_lkl_ggh _]h kbeZly]bl_f[uklj__hgm_ebqbZ_lkhxkdhjhklv3. Hiul bah[jZ`_gguc gZ jbkmq_[gbdZ ^hdZauZ_l lh qlhijbeh`_ggZy d l_em kbeZ yey_lky ijbqbghc mkdhj_gby eyijh_^_gby^Zggh]hhiulZgZ^haylvl_e_`dmmklZghblvgZg_c^Zh^bgZdhhjZ[hlZxsbo_glbeylhjZb dZi_evgbpmeydhfi_gkZpbbkbeulj_gbyijbdj_ibfd l_e_`d_h^bgbadhgphgblbi_j_dbgmlhcq_j_a [ehd Z d ^jm]hfm dhgpm gblb ih^_kbf ]jma AZl_f hldjh_fdjZg dZi_evgbpu b dexqbf h[Z _glbeylhjZ Ih^ ^_cklb_f kbeu_glbeylhjh l_e_`dZ ijb^_l^b`_gb_ Ijb wlhf gZ klhe [m^mliZ^Zlv dZieb q_j_a h^bgZdhu_ ijhf_`mldb j_f_gb L_i_jv _kebbaf_jylvjZkklhygbyf_`^mkhk_^gbfbdZieyfblhfh`ghm[_^blvkyqlh wlb jZkklhygby [m^ml hlghkblvky dZd jy^ ihke_^hZl_evguog_q_lguo qbk_e LZdbf h[jZahf fh`gh aZdexqblv qlh l_e_`dZ^b]ZeZkvjZghmkdhj_gghkf 19. IhkqblZ_fmkdhj_gb_ihnhjfme_a = 2aZf_jb ijhc^_ggh_ l_e_`dhc jZkklhygb_ s b j_fy __2s^b`_gby t ?keb mf_gvrblv kbem ^_cklmxsmx gZ l_e_`dm^Z tjZaZ udexq_gb_f h^gh]h ba _glbeylhjh 20. b kghZ ihkqblZlvmkdhj_gb_ lh hgh ihemqblky^Z jZaZ f_gvrbf q_f i_juc jZa?keb l_i_jv m_ebqblv fZkkm l_e_`db^Z jZaZ ^h[Ze_gb_f dl_e_`d_ ]jmaZ fZkkhc jZghc fZkk_ l_e_`db 21. b kghZ ihkqblZlv 10 22. mkdhj_gb_ lh hgh ihemqblky^Z jZaZ f_gvrbf q_f i_juc jZaLZdbf h[jZahf aZdexqZ_f qlh mkdhj_gb_ l_e_`db ijyfhijhihjpbhgZevgh ijbeh`_gghc d g_c kbe_ b h[jZlghijhihjpbhgZevgh__ fZkk_4. Mkdhj_gb_ l_eZ ijyfh ijhihjpbhgZevgh jZgh^_cklmxs_cijbeh`_gguo d g_fm kbe b h[jZlgh ijhihjpbhgZevgh _]h fZkk_ 7 7 Fa= . d] fm5. HgbkhgZijZe_gu6. G 1 2 .k 12.1. Hiulubah[jZ`_ggu_gZjbkmq_[gbdZih^l_j`^Zxllj_lbc aZdhg GvxlhgZ h k_o wlbo hiulZo ijb ihfhsb ^mo^bgZfhf_ljh baf_jyxlky kbeu k dhlhjufb ^Z l_eZ ^_cklmxl^jm]gZ^jm]Z i_jhfhiul_aZbfh^_cklb_l_eijhbkoh^blijbbo g_ihkj_^kl_gghf dhglZdl_ h lhjhf gZ jZkklhygbb lj_lv_f ijhp_kk_ ^b`_gby Ijb wlhfdZ`^hf kemqZ_ihdZaZgby ^bgZfhf_ljh hdZauZxlky h^bgZdhufb LZdbfh[jZahf fh`gh k^_eZlv uh^ qlh ^Z l_eZ ^_cklmxl ^jm] gZ^jm]Z k kbeZfb jZgufb ih fh^mex b ijhlbhiheh`gufb ihgZijZe_gbx2. Kbeuk dhlhjufbaZbfh^_cklmxl^Zl_eZjZguihfh^mexbijhlbhiheh`guihgZijZe_gbx3. Wlhmkdhj_gb_b^m[hevrhcfZkkuA_febij_g_[j_`bl_evghfZeh4. GZijbf_j Khegp_ b EmgZ aZbfh^_cklmxl ihkj_^klhf]jZblZpbhgguokbe5. Wlbkbeuijbeh`_gud jZagufl_eZf1. b`_gb_ih^^_cklb_fkbeuly`_klb 13.2. GZ^h baf_jblv jZkklhygby dhlhju_ rZjbd ijhoh^bl aZihke_^hZl_evgu_ h^bgZdhu_ ijhf_`mldb j_f_gb b m[_^blvky lhf qlh ^Zggu_ jZkklhygby hlghkylky dZd jy^ ihke_^hZl_evguog_q_lguo qbk_e Wlh b [m^_l yeylvky ^hdZaZl_evklhf lh]h qlhkh[h^gh_iZ^_gb_l_eZyey_lkyjZghmkdhj_gguf^b`_gb_fkf3. K p_evx ihdZaZlv qlh mkdhj_gb_ kh[h^gh]h iZ^_gby h^bgZdhh8).^eyk_ol_e4. Mkdhj_gb_uaZggh_^_cklb_fkbeuly`_klb5. BaaZkbeukhijhlbe_gbyha^moZ 11 23. 6. =Zebe_c14.1. ZhgZij_iylklm_l_]hih^t_fm2. K mkdhj_gb_f g Ijb ^b`_gbb l_eZ _jo _]h kdhjhklvmf_gvrZ_lky ih aZdhgm v(t) = v0 gt_jog_c lhqdb ljZ_dlhjbbkdhjhklv l_eZ jZgZ gmex b hgh gZqbgZ_l ^b]Zlvky gbam_ebqbZykdhjhklvihaZdhgmv(t) = gt^hl_oihjihdZg_ miZ^_lgZa_fex3. Hl_ebqbgugZqZevghckdhjhklb4. ?keb gZijZblv hkv _jo lh ijh_dpby _dlhjZ kdhjhklb gZ wlmhkv iheh`bl_evgZ Z ijh_dpby mkdhj_gby kh[h^gh]h iZ^_gby hljbpZl_evgZ15.1. aZbfgh_ ijbly`_gb_ k_o l_e k_e_gghc ]jZblZpbhggh_aZbfh^_cklb_l_e 24. 2. =jZblZpbhggufb3. BkZZdGvxlhg ;9,,_d_4. Z l_eZ ijbly]bZxlky ^jm] d ^jm]m k kbehc ijyfhijhihjpbhgZevghc ijhba_^_gbx bo fZkk bh[jZlghijhihjpbhgZevghcdZ^jZlmjZkklhygbyf_`^mgbfb5. F = G 1 2 2]^_ F fh^mev ]jZblZpbhgghc kbeu m1, m2 mmfZkku aZbfh^_cklmxsbo l_e r jZkklhygb_ f_`^m gbfb G r]jZblZpbhggZyihklhyggZyjZgZy 10-11 Gf2d]2.6. AZdhgk_fbjgh]hly]hl_gbykijZ_^eb ke_^mxsbokemqZyo 25. ^ey^mol_ejZaf_judhlhjuoij_g_[j_`bfhfZeuk jZkklhygb_frf_`^mgbfb 26. _kebh^ghbal_ebf__lnhjfmrZjZjZ^bmkb fZkkZdhlhjh]h h fgh]h jZa [hevr_ q_f m lhjh]h l_eZ ijhbahevghcnhjfu 27. ^ey ^mo h^ghjh^guo l_e rZjhh[jZaghc nhjfu ijbex[uobojZaf_jZo7. Z1. _jgh 2. Mf_gvrZ_lky3. Fl = mg.16.4. KbeZly`_klb[hevr_gZ ihexkZoldA_fey g_fgh]hkiexkgmlZm ihexkh5. Hghijb[ebabl_evgh jZaf_gvr_a_fgh]h12 28. 1. RZjbd ^b`_lky hl lhqdb : d lhqd_ih^ ^_cklb_f kbeu18. 7mijm]hklb FWlZ kbeZ hagbdeZj_amevlZl_ jZkly`_gby rgmjZKdhjhklv mkdhj_gb_ rZjbdZ b ^_cklmxsZy gZ g_]h kbeZgZijZe_gu hl lhqdb A d lhqd_ B RZjbd ^b`_lky ijyfhebg_cghl__]hljZ_dlhjbyijyfZyebgby2. 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Ihweebilbq_kdhchj[bl_hdjm]A_febihweebilbq_kdhchj[bl_hdjm]KhegpZ13 29. 21.1. Bfimevkhf l_eZ gZauZ_lky nbabq_kdZy _ebqbgZ jZgZyijhba_^_gbxfZkkul_eZgZ_]hkdhjhklv2. Bfimevkb kdhjhklv^b`ms_]hkyl_eZk_]^ZkhgZijZe_gu3.kbkl_f_KBd]fk22.1. Hiul bah[jZ`_gguc gZ jbkmgd_mq_[gbdZ ijhh^blkyke_^mxsbfh[jZahf;_jmlky^ZrZjbdZih^_r_ggu_gZgblyolZdqlh[u hgb dZkZebkv ^jm] ^jm]Z H^bg ba rZjbdh hldehgyxl gZg_dhlhjuc m]he b hlimkdZxl RZjbd ^hklb]gm kh_]h ij_`g_]hiheh`_gby m^Zjy_lky h lhjhc b hklZgZebZ_lky Ijb wlhf lhjhcrZjbd hldehgy_lky gZ lhl `_ m]he LZdbf h[jZahf ijbaZbfh^_cklbbbfimevki_jh]hrZjbdZmf_gvrbekygZklhevdhgZkdhevdhm_ebqbekybfimevklhjh]hWlhlhiulih^l_j`^Z_laZdhgkhojZg_gbybfimevkZ2. 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Hiul klZbeky k p_evx ihdZaZlv qlh dhe_[Zgby ijm`bggh]hfZylgbdZyeyxlky]Zjfhgbq_kdbfbHgaZdexqZ_lky lhfqlh]jmagZijbf_j hjhgdZ k gZeblhc djZkys_c `b^dhklvx 41. mdj_ie_ggucgZ ijm`bg_ ijb kh_f dhe_[Zl_evghf ^b`_gbb hklZey_l ke_^ljZ_dlhjbb gZ ^b`ms_cky k ihklhygghc kdhjhklvx [mfZ`ghce_gl_ Ihemq_ggZy lZdbf kihkh[hf ljZ_dlhjby yey_lkykbgmkhb^hc2. Kbgmkhb^hc Hlj_ahd OA khhl_lklm_l Zfieblm^_ dhe_[Zgbc Zhlj_ahdOB i_jbh^m3. =Zjfhgbq_kdbfb dhe_[Zgbyfb gZauZxlky dhe_[Zgbydhlhjuobaf_g_gb_dZdhceb[h nbabq_kdhc _ebqbgu ijhbkoh^bl ih aZdhgmkbgmkZbebdhkbgmkZ4. Qlhdhe_[Zgbygbl_h]hfZylgbdZyeyxlky]Zjfhgbq_kdbfb5. FZl_jbZevgZy lhqdZ h[eZ^ZxsZy fZkkhc b dhe_[exsZyky gZihklhygghf jZkklhygbb hl lhqdb ih^_kZ gZauZ_lkyfZl_fZlbq_kdbffZylgbdhf16 42. 6. Dhe_[Zgby gblygh]h fZylgbdZ fh`gh kqblZlv ]Zjfhgbq_kdbfb_keb^ebgZgblbfgh]h[hevr_jZaf_jhih^_r_ggh]hgZg_cl_eZgZijbf_j rZjbdZ 43. gblv hq_gv e_]dZy b fZehjZkly`bfZy kbeulj_gby kbkl_f_hlkmlklmxlZfieblm^Zdhe_[ZgbcfZeZ7. F_gyxlkyihaZdhgmkbgmkZbebdhkbgmkZ28.1. 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Ijhl_dZgb_ l_jfhy^_jguo j_Zdpbc hafh`gh lhevdh ijb hq_gvukhdbo l_fi_jZlmjZo ld g_h[oh^bfh ijb^Zlv y^jZf ^hklZlhqgh[hevrmxdbg_lbq_kdmxwg_j]bx^eybok[eb`_gbygZhq_gvfZeu_jZkklhygbyijbdhlhjuohafh`ghbokebygb_ 37 109. 3. Kebygb_e_]dboy^_j4. 2 H + 3 H 4 He+ 0 n . 15. HkghgZy ljm^ghklv ijb hkms_kle_gbb l_jfhy^_jghc j_Zdpbb 1 1 2aZdexqZ_lkylhf qlh[u m^_j`Zlv ukhdhl_fi_jZlmjgmx ieZafmgmljb mklZghdb ?keb ieZafZ dhkg_lky kl_ghd mklZghdb dhlhjhchgZgZoh^blkylhhgbjZkieZylkyb ij_jZlylky iZj6.j_amevlZl_ l_jfhy^_jguo j_Zdpbc ijhl_dZxsbo gZ Khegp_u^_ey_lkywg_j]byg_h[oh^bfZy^ey`bagbgZA_fe_38 110. MijZ`g_gbyMijZ`g_gb_ 1. Fh`ghh[hbo kemqZyo ld jZaf_jZfb Zlhfh[bey ijb ^ZgguogZqZevguomkehbyofh`ghij_g_[j_qv2. k_aZbkblhlmkehbcaZ^Zqdhlhju_gm`ghj_rblv^bki_lq_jmb iZkkZ`bjm3. Ih_joghklvA_feb4. IjZ b fZevqbd b ^_hqdZ FZevqbd u[jZe kbkl_fm hlkq_lZkyaZggmxk a_fe_c^_hqdZk dj_kehfdZjmk_eb5. Z 111. hlghkbl_evgh A_feb [ 112. hlghkbl_evgh h^u 113. hlghkbl_evghA_feb] 114. hlghkbl_evghhkbdhe_kZ^ 115. hlghkbl_evghA_febMijZ`g_gb_ 1. Ijhc^_ggucimlv2. Ijyfhebg_cghMijZ`g_gb_ 771.s sf xxfx = xk + so = 10 df + (2 df) = 8 df;Oxcxf = xk + sfo dfdf df2. Z 116. o0 f[ 117. sto = s1o + s2o f f 118. f 119. xt = o0 + sto f f fMijZ`g_gb_ 1. =jZnbd fh^mey _dlhjZ kdhjhklb g_ fh`_l gZoh^blvky ih^ hkvxijh_dpbb _dlhjZ kdhjhklb fh`_l gZoh^blvky ih^ hkvx Ot,Otihkdhevdmfh^mev_dlhjZkdhjhklbk_]^Ziheh`bl_e_g=jZnbdihkdhevdm agZd aZbkbl ijh_dpbb _dlhjZ kdhjhklb hl u[hjZkbkl_fudhhj^bgZl vx, dfq2.8060tq 90 39 120. MijZ`g_gb_ 1. I_juc Zlhfh[bev ^b]Zeky k [hevrbf mkdhj_gb_f ihkdhevdm_]hkdhjhklvaZh^bgZdhu_ijhf_`mldbj_f_gbhajZklZeZ[uklj__ZghJ_r_gb_2.55 fk 10 fkv1 fk= 1,5 fk 2 .t = 30 c v v30 k a= 2 1 =v2 fktGZclbZ. Hl_la fk2.ZghJ_r_gb_3.6 fkv2 v1 fk= 0,5 fk 2 .t = 12 c v v12 k a= 2 1 =GZclbZ. Hl_la fk2.t MijZ`g_gb_ Zgh J_r_gb_1.v1 fk v va = 2 1 v2 = v1 + at =a = 20 fk2t=4c fk fk2) k fk tGZclb v2. Hl_lv2 fkZgh J_r_gb_2.a fk2 2 fk= 10 k v vv va 0,2 fk 2a= 2 1 = 2 t = 2 =v2 fkv1 = 0 ttGZclbt.Hl_lt k Y[3. W 40 121. 4. vx5 -5510 t5. eyl_eZ,Z fk2^eyl_eZ,,Z fk2. MijZ`g_gb_ Zgh J_r_gb_1. 0,5 fk 2 (5 k )Zo fk2fk kt=5caxt 22sx = v0 o t +v0o dfq fk= f 22GZclbsx. Hl_lsx fZghJ_r_gb_2.Zo fk2t = 20 caxt 2 v v t2 v t sx = v0 o t +; ao = 0 x sx = v0 o t 0 x = 0 x =v0o fkfk kf 2t 2t 2GZclbsx.Hl_lsx f MijZ`g_gb_ ZghJ_r_gb_1.s3 fs1 : s2 : s3 = 1 : 3 : 5; s1 : 2 f = 1 : 5 s1 = 2 f 5 = 0,4 f;t1 k2 0,4 f= 0,8 f/k2. 2at1 2s (1 k) s1 = a = 21 = 2 2GZclb s1, a. Hl_ls1 fa fk2. t1ZghJ_r_gb_2.s5 fs1 : s2 : s3 : s4 : s5 = 1 : 3 : 5 : 7 : 9; s1 : 6,3 f = 1 : 9 t1 k s1 = 6,3 f 5 = 0,7 f;t5 k 2 0,7 f = 1,4 f/k2;2at12s(1 k)2 s1 = a = 21 = 2 v5 = at5 fk2 k fkt1GZclbv5.Hl_lv5 fk41 122. MijZ`g_gb_ 1. fk2. G_l ihkdhevdm b ^_j_h b hdaZe `_kldh kyaZgu k ^jm]hckbkl_fhchlkq_lZA_fe_c3. Ijbmkehbbg_ih^b`ghklbwlbol_ehlghkbl_evgh^jm]^jm]Z4. dfq fkZghJ_r_gb_5*.v1 dfq fkv = v1 + v2 fk fk fkv2 fkva = v2 v1 fk fk fkGZclbv, va.Hl_lv fkva fkMijZ`g_gb_ AZdhgbg_jpbbuihegy_lky kbkl_f_hlkq_lZkyaZgghck A_fe_cb kbkl_f_ hlkq_lZ kyaZgghc k ih_a^hf h j_fy _]hijyfhebg_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`_gbyBg_jpbZevghckbkl_fhcfh`ghkqblZlva_fexZ ih_a^g_evayMijZ`g_gb_Zgh J_r_gb_1.Z fk2 IhhfmaZdhgmGvxlhgZm d]F = ma d] fk2 GGZclbF.Hl_lF GZghJ_r_gb_2. F = ma hcaZdhgGvxlhgZv fkt = 20 cmv 1,84 10 5 d] 4 fkm l 10 d] 20 kv5a= F=== G dGttGZclbF. Hl_lF dGZghJ_r_gb_3. IhhfmaZdhgmGvxlhgZa1 fk2 F1 = m1a1; F2 = m2a2. Ldm1 = m2lhihemqZ_fm1 = m2a2 fk2 F1 F2 a F 0,64 fk 2 1,2 G0,08 fk 2F1 = 1,2 H= F2 = 2 1 = = 9,6 H.a1 a 2 a1GZclbF2. Hl_lF2 G42 123. ZghJ_r_gb_4.m = 0,5 d] IhhfmaZdhgmGvxlhgZF = ma.FA = 10 HF = FA FL FC FA FL FC = ma fk2.FL = 5 H F FL FC 10 H 5 H 2 H0,5 d]FC = 2 H a = A=GZclbF2.Hl_la fk2.m5. Ijb ^b`_gbb _jo kdhjhklv b i_j_f_s_gb_ ijhlbhiheh`ghgZijZe_gu k kbehc ly`_klb mkdhj_gb_ khgZijZe_gh Ijb^b`_gbbgbakdhjhklvi_j_f_s_gb_b mkdhj_gb_khgZijZe_gukkbehcly`_klb6. Mkdhj_gb_ k_]^Z khgZijZe_gh k jZgh^_cklmxs_cijbeh`_gguo d l_em kbe Kdhjhklv b i_j_f_s_gb_ fh]ml [ulv dZdkhgZijZe_gu k jZgh^_cklmxs_c ijbeh`_gguo d l_em kbe lZd bijhlbhiheh`ghgZijZe_gu MijZ`g_gb_ 771. GZ l_eh ^_cklmxl kbeZ ly`_klb Fl b kbeZ j_Zdpbb hihju Nkfjbk 124. 7N7Fl2. G_ ij_ukbl ld jZgh^_cklmxsZy ijbeh`_gguo kbe gZ^bgZfhf_ljjZgZZghJ_r_gb_3.m1 d] 125. IhhfmaZdhgmGvxlhgZm2 d] F2x = m2ax d] fk2 Ga fk2 IhfmaZdhgmGvxlhgZF1x = F2x G 126. IhhfmaZdhgmGvxlhgZ F1x = m1ax d] fk2 G IhfmaZdhgmGvxlhgZF2x = F1x G 127. i_jhf kemqZ_ gblv f_`^m l_e_`dZfb gZlygmlZ kbevg__ 128. IhhfmaZdhgmGvxlhgZ Fx = (m1 + m2)ax d]d] 129. fk2 GGZclb F1x, Hl_l 130. F1x GF2x G 131. F1x GF2x =F2x, Fx.G 132. i_jhfkemqZ_ 133. Fx G 43 134. MijZ`g_gb_ZghJ_r_gb_1.g fk2 gt 2 10 fk 2 (2 k )f2t=2c h==GZclbh. Hl_lh f 2 2Zgh J_r_gb_2.g fk2 2 0,8 fh = 80 cf f= 0,4 k. gt 210 fk 2 2hh=t= =GZclbt.Hl_lt k2gZghJ_r_gb_3.g fk2 2 45 fh = 45 f kgt 210 fk 2 2h h=t== 2 ggt1 10 fk 2 (1 k )2t1 = 1 c = 5 f;t = 1 c 2 s1 = =gt 2 g (t t ) 2 2 2 s2 = = 10 fk 2 (3 k ) 10 fk 2 (3 c 1 c ) 2 2=5f2 2 =GZclb t, s1, s2. Hl_lt ks1 fs2 f 22MijZ`g_gb_ZghJ_r_gb_v fkv v1 v9,8 fk g 9,8 fk 2 v= t= =g fk2v1 = 0 g==1 c;tt9,8 fk 2 (1k )fk k f2 gt 2 s = vt GZclbt, s.Hl_lt ks f22MijZ`g_gb_1. k_l_eZiZ^ZxlgZa_fexih^^_cklb_fkbeuly`_klb2. KlZgpby m^Zey_lky hl A_feb ijb[eb`Zykv d Emg_ BaaZbaf_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_44 135. m_ebqbZ_lky Dh]^Z klZgpby gZoh^blky gZ k_j_^bg_ hgZ kbevg__ijbly]bZ_lkyd A_fe_ldfZkkZA_feb[hevr_fZkkuEmgu3. G_l4. Z 136. ^_cklhZeZ[ 137. ijbly`_gb_A_feb 138. baaZ^_cklbykbeuly`_klb5. Zijbly]bZ_lky ghwlZkbeZ]hjZa^hf_gvr_kbeuly`_klb baaZjZkklhygbcEmgZlZd`_ijbly]bZ_lkyd wlhfmq_eh_dmMijZ`g_gb_Zgh J_r_gb_1.g fk2 Fl = mg m1 d]Fl fk2 d] Gm2 ] d] Fl fk2 d] Gm3 l d]Fl fk2 d] G dGm4 l d]Fl fk2 d] 105 G dGGZclb Fl1, Fl2, Fl3, Fl4. Hl_lGGdGdGZgh J_r_gb_2.g fk2; m d] Fl = mg d] fk2 GGZclbFl. Hl_lFl GZgh J_r_gb_3.g fk2; Fl 819,3 GFl Gd] g 10 fk 2Fl = mg m ==GZclbFl. Hl_lm d]4. G_lihkdhevdmukhlZihe_lZkjZgbfZk jZaf_jZfbA_febKbem F a mjly`_klb fh`gh jZkkqblZlv ih nhjfme_ Fl = G]^_ h ( Ra + h) 2ukhlZgZ^A_fe_c5. GZyklj_[Z^_cklm_lkbeZly`_klbb _kebhgkeh`bldjuevylhhgmiZ^_lgZA_fex6. GZjZkklhygbbRa; 3Ra (Ra jZ^bmkA_feb 139. ihkdhevdmFl~ 1 (Ra + h)2MijZ`g_gb_ 71. KbeZ F fh]eZ^_cklhZlvlhevdh gZijZe_gbb2. KbeZ ^_cklhZeZ gZ rZjbd gZ mqZkldZoRZjbdihhjZqbZekyih^^_cklb_fg_rgbokbe3. KbeZ^_cklhZeZgZl_ehgZ_jgydZgZmqZkldZo:GZl_ehfh]eZ^_cklhZlvkbeZb gZhklZevguomqZkldZo 45 140. MijZ`g_gb_Zgh J_r_gb_1.r kf fv 2 (20 fk )2v fk Z= fk2.0,21 f =GZclba.Hl_lZ fk2.rZgh J_r_gb_2.R kf fT k Z= Z= 2 = 2 =v2l 2R 4 2 R 2 4 2 R ;v= =RTT4 (3,14 ) 0,02 f T RT 210-4 fk2. 2 (60 k )2=GZclba.Hl_lZ 210-4 fk2.3. Z1 =; Z2 = = 2a1 ml_j`^_gb__jghv2v2 v2= 2 rr/2 rZgh J_r_gb_4.T1 kT2 k. :gZeh]bqgh a 2 =v 2 (2R T1 )2 4 2 R4 2 Ra1 = 1 == 2. RR T1T22 Ke_^hZl_evgh2 a1 T1 2 3600 c = =T = 3600. a2 2 60 c GZclbHl_la1a1 . = 3600.a2a2ZghJ_r_gb_5.Fa = 61024 d]F aF eG f2Fe = 61022 d] Z 141. F]j = Gd] 2= 6,6710-11 G f2 26 10 24 d] 7 10 22 d] r d] 2 1,91020 GG=6,6710-11(3,84 10 8 f 142. 2r = df= 3,84108 f 1,9 10 20 G [ 143. Zp = 3,1710-5 fk2; F]j Fa6 10 24 d] = 144. v = ap r = 3,17 105 fk2 3,84108 f fkGZclbF]j, Zp, v.Hl_lF]j 1,91020 Gv fk Zp = 3,1710-5 fk2. 46 145. MijZ`g_gb_ZghJ_r_gb_1.h df 106 f MaFa = 61024 d] v G =Ra = 6,4106 f Ra + h G f2G f2 6 1024 d]d] 2(2,6 106 f + 6,4 106 f 146. = 6,67 1011d] 2G = 6,6710-11= fk dfkGZclbv.Hl_lv dfkZghJ_r_gb_2.v dfk 103 fk 1,67 10 3 fk( )ge fk2 2v2v21,6 fk 2 re = re === re ge = 1,7106 f 103 dfGZclb re.Hl_lre = 1,7103 dfMijZ`g_gb_Zgh J_r_gb_1.v1x = v2x fk p1x = mv1x d] fk d]fkm = 0,2 d]p2x = p1x d]fk_dlhjubfimevkhfZrbgg_jZguldhgbijhlbhiheh`ghgZijZe_gu Fh^meb_dlhjhbfimevkhjZguGZclb p1x, p2x. Hl_lp1x d]fkp2x d]fkZgh J_r_gb_2.v1 dfq fkv2 dfq fkj = mv = m(v2 v1) = d] fk fk 147. d]fkm l d]GZclb p. Hl_lp d]fkMijZ`g_gb_1. Ih aZdhgm khojZg_gby bfimevkZ eh^dZ gZqg_l ^b]Zlvky klhjhgmijhlbhiheh`gmx^b`_gbxq_eh_dZ 47 148. Zgh J_r_gb_2.m1 lAZibr_faZdhgkhojZg_gbybfimevkZm2 lv2 fk m + m2m1v1 = (m1 + m2)v2 v1 = 1 v2 =35 l + 28 l m1= 0,5 fk fkGZclb v1. Hl_lv1 fk 35l MijZ`g_gb_Zgh J_r_gb_1.ve fk AZibr_faZdhgkhojZg_gbybfimevkZm d](me + m)ve + mv = mev v = e ( m + m ) v e + m v v fkme d] = me(200 d] + 5 d] ) 2 fk + 5 d] 8 fk fk200 d]=GZclb v.Hl_lv fkZgh J_r_gb_2.mj ] d] AZibr_faZdhgkhojZg_gbybfimevkZmi ] d]0,1 d] 100 fkvi fk mjvj=mivivj= i i = fk0,3 d]m v mjGZclb vj. Hl_lvj fk MijZ`g_gb_1. Dhe_[Zl_evgufb kbkl_fZfb yeyxlky [ ] _ G_ yeyxlkydhe_[Zl_evgufbZ^2. Z 149. Ih^^_cklb_fkbemijm]hklbrgmjh[ 150. g_l 151. rgmju^bkd] 152. ^Zyey_lky MijZ`g_gb_1. :fieblm^Z : qZklhlZ i_jbh^ L ihklhyggu_ F, v i_j_f_ggu_Zgh J_r_gb_2. = =p= 0,5 k 2 =p 11T= =GZclb T.Hl_lT k 48 153. Zgh J_r_gb_3.T k= 2 =p 1 1= =GZclb .Hl_l =p T 0,5 cZgh J_r_gb_4.t fbg k= 10 =pn = 6001 tn 600= ; T = = =GZclb .Hl_l =p T nt 60 c5. kfkfkfkfZgh J_r_gb_6.A = 10 kf = 2 c AZk l_eh kh_jrZ_l ihegh_ = 0,5 =p 0,5 =p 11T = =t kdhe_[Zgb_b ijhc^_limlvS = 4: kfGZclb S.Hl_lS kf7. Dhe_[exlkyh^bgZdhuo nZaZokemqZyo [ 154. ^ 155. Dhe_[exlky ijhlbhiheh`guonZaZo kemqZyoZ 156. ] 157. _ 158. MijZ`g_gb_GZijZ ?i?d ?ihe1.Fmij e_gb_K lj_ ;_a lj_v ^b`_gby gb_fgby fZylgbdZ Hl d H mf_gvm_emf_gvm_emf_gv g_ baf_g HlH d : m_e mf_gvm_e mf_gv mf_gv g_ baf_g Hl: d H mf_gvm_emf_gvm_emf_gv g_. baf_g HlH dm_e mf_gvm_e mf_gv mf_gv g_ baf_g2. Z 159. `` [ 160. ``` 161. ` h k_o.kemqZyo MijZ`g_gb_1. Kihkh[gu kh_jrZlv kh[h^gu_ dhe_[Zgby l_eZ [ 162. _ 163. ugm`^_ggu_dhe_[Zgbyk_l_eZ2. Z 164. ^ZgZijbf_jkljmgZfmaudZevgh]hbgkljmf_glZ[ 165. g_l49 166. MijZ`g_gb_1. Z 167. ugm`^_ggu_[ 168. [eZ]h^Zjydhe_[ZgbxfZylgbdZ 169. qZklhlZfZylgbdZ jZgZ qZklhl_ fZylgbdZm fZylgbdZqZklhlZ [hevr_q_fm fZylgbdZm fZylgbdZqZklhlZf_gvr_q_fm fZylgbdZ] 170. ldbo^ebgub khhl_lkl_gghkh[kl_ggu_qZklhlukhiZ^Zxl2. FZevqbdb h^ZgZqbgZxldhe_[Zlvky ijhlbhnZa_3. Q_j_ak L = 1/ k 171. MijZ`g_gb_Zgh J_r_gb_1. f 270 f= 20 fkT kT 13,5 kv= =GZclb v.Hl_lv fkZgh J_r_gb_2. =p v 340 fk = 1,7 fv fk 200 =p= =GZclb .Hl_l f3.Zgh J_r_gb_2.v fk6f= 4 k f T 1,5 fkv= =GZclbT.Hl_lT = 4 c.MijZ`g_gb_E_lysZyilbpZkha^Z_lbgnjZamdhu_heguMijZ`g_gb_1. DhfZjAmdkha^ZZ_fucbfkZfucukhdbc2. Mf_gvrblkyihkdhevdmqZklhlZ__ jZs_gbylZd`_mf_gvrblky3. Ijb ihur_gbb l_fi_jZlmju kljmgZ jZkly]bZ_lky i_jbh^ __dhe_[Zgbc m_ebqbZ_lky qZklhlZ b khhl_lkl_ggh ukhlZamqZgbymf_gvrZ_lkyMijZ`g_gb_1. G_lf_`^mA_fe_cb Emghcg_lmijm]hckj_^uihdhlhjhcfh`_ljZkijhkljZgylvkyamd2. Amdhu_hegujZkijhkljZgyxlkyihgblb50 172. MijZ`g_gb_ZghJ_r_gb_1. f2,9 f= 1450 fkT kT 0,002 k v= =GZclb v. Hl_lv fkZgh J_r_gb_2.v1 fkv 340 fk1483fkv2 fk 0,47 f; 2 = 2 = 2,05 f; 725 =p725 =pv1 = 1 =v3 fk 5500 fk =p 7,59 f. 725 =p v3 = 3 =GZclb1, 2, 3. Hl_l1 f2 f3 f3. Amd [m^_l jZkijhkljZgylvky b ih f_lZeem b ih ha^mom bq_eh_dmkeurbl^Zm^ZjZZghJ_r_gb_4.ta k Sa = vata; SiZj = viZjtiZj; Sa = SiZj; vata = viZjtiZj va fk 340 fk 2 ktiZj k viZj = a a == 20 fk 34 kv t t iZjSa = SiZjGZclbviZj.Hl_lviZj fk5. Dh]^Zb^bfu_b keurbfu_m^ZjugZqbgZxlkhiZ^ZlvkghZlhwlhagZqblqlhq_eh_dkeurblij_^u^msbci_j_^b^bfufm^ZjMijZ`g_gb_1. Kms_klm_l2. FZ]gblgh_ ihe_ [m^_l ^_cklhZlv gZ klj_edm k gZb[hevr_ckbehclhqd_ N k gZbf_gvr_c lhqd_ F K jZkklhygb_ffZ]gblgh_ihe_hkeZ[_Z_lMijZ`g_gb_1. Z 173. ?klvwlhlhqdbD b K[ 174. lhqd_:. 3GZ iZju lhq_d P Q, X Y kh2.klhjhgu g_h^ghjh^gh]h fZ]gblgh]hihey ^_cklmxl kbeu h^bgZdhu_ ,dZd ih fh^mex lZd b ih2gZijZe_gbx ld PO = QO, XO = ,;YO. 451 175. MijZ`g_gb_1.2.3. K__jguc ihexk gZoh^blky kijZZ Z x`guc ke_Z Boiheh`_gb_fh`ghbaf_gblvihf_gyiheyjghklvkhe_ghb^Z4. Lhd[m^_ll_qvhllhqdbS d lhqd_N.5. KijZZ k__jguc ihexk ke_Z x`guc ih ijZbem ijZhcjmdb 176. 6.i_jhf kemqZ_ aZbfh^_cklb_ h[mkehe_gh fZ]gblgufbkbeZfbhlhjhfdmehghkdbfb MijZ`g_gb_1. IhijZbeme_hcjmdbhij_^_ey_fqlhijZh2. Ih ijZbem e_hc jmdb hij_^_ey_f qlh lhd l_q_l hl lhqdb B dlhqd_ A b ke_^hZl_evgh _jogbc ihexk bklhqgbdZ lhdZih^dexq_g d hljbpZl_evghfm ihexkm Z gb`gbc diheh`bl_evghfm52 177. 3. GZ e_hf jbkmgd_ e_uc ijhh^gbd ^b`_lky _jo ijZucijhh^gbdgbaGZijZhfjbkmgd_e_ucijhh^gbd^b`_lkygbaijZucijhh^gbd_jo4. 77 vF5. Ih ijZbem e_hc jmdb hij_^_ey_f qlh wlh iheh`bl_evghaZjy`_ggZyqZklbpZ MijZ`g_gb_Zgh J_r_gb_1. 0,2 Gl kf f= 0,5 Le Il 0,1 f 4 :I = 4 A; F = 0,2 H F B= =GZclbB.Hl_lB Le2. FZ]gblgZy bg^mdpby g_ baf_gy_lky hgZ ihklhyggZy _ebqbgZBaf_gy_lkylhevdhkbeZ^_cklmxsZygZijhh^gbdhgZlZd `_dZdb lhdmf_gvrZ_lky jZaZ MijZ`g_gb_FZ]gblguc ihlhd ijhgbauZxsbc dZlmrdm D2 fh`gh f_gylviml_fbaf_g_gbyaZbfghchjb_glZpbbdZlmr_db baf_g_gb_fkbeulhdZj_hklZlhfR bebaZfudZgb_fjZafudZgb_fdexqZD MijZ`g_gb_1. Baf_gblvfZ]gblgucihlhdq_j_adZlmrdmD2 iml_fhibkZggufmijZ`g_gbb2. Bg^mdpbhgguclhdhagbdZ_l kemqZ_] 178. g_hagbdZ_l kemqZyoZ 179. [ 180. ^ 181. MijZ`g_gb_Zgh J_r_gb_1.53 182. =p= 0,02 k 50 =p 1 1T= =GZclb T. Hl_lT k2. Ih]jZnbdmgZoh^bfqlhT=k , = = =p111 T (1 60 )c: f:60 MijZ`g_gb_Wlbiheygbq_fg_hlebqZxlkyb kms_klhZeb[u[_adZlmrdbK MijZ`g_gb_Zgh J_r_gb_1. = = 7 = 10 7 =pT = 10-7 c 11GZclb.Hl_l = 107 =p T 10 cZgh J_r_gb_2.S = ct = 3108 fk 8,310-7 k fc = 3108 fkt = 8,310-7 cGZclb S.Hl_lS = 249 fZgh J_r_gb_3. f c 3 108 fkc = 3108 fk= 5 105 =p600 f= =GZclb.Hl_l = 5105 =p4. AgZy kdhjhklv jZkijhkljZg_gby kb]gZeZ k hgZ jZgZ kdhjhklbk_lZ 183. b j_fy _]h jZkijhkljZg_gby t g_ljm^gh jZkkqblZlvijhc^_ggh_ jZkklhygb_ S AZ j_fy t kb]gZe ijhc^_l jZkklhygb_ Slm^Zb h[jZlghbke_^hZl_evghS = ct/2.5. G_lamdhu_hegug_jZkijhkljZgy_lky Zdmmf_ MijZ`g_gb_1. 12 K Z_f 6 Li Z_f 40 Ca Z_f6 3202. 6, 3, 20.54 184. 6 Z_f3.n =jZa1 Z_f4. Z 185. [ 186. Z_f 187. jZa] 188. ^ 189. _ 190. ` 191. 5. 14 K 140 O + 0 _ 14 O =14 N Zahl66+117 7 MijZ`g_gb_ 7 N + 2 He 8 O +1 HBf__f Ke_^hZl_evgh14 4 171aZdhgkhojZg_gbyaZjy^Zuihegy_lky MijZ`g_gb_1.y^j_ ZlhfZ [_jbeeby 9 Be gmdehgh ijhlhgh g_cljhghN = A + Z = 9 4 = 5. 42. 39 DZ 192. Z [ 193. Np = Z 194. Qwe_f_glZjguowe_dljbq_kdboaZjy^Zo 195. ] 196. Ne = Np ^ 197. _ 198. ` 199. : a 200. N = 19 b 201. m Z_fAZ=3. Qbkeh ijhlhgh khhl_lkl_ggh we_dljhgh 202. Zlhf_ jZgh _]hihjy^dhhfm ghf_jmlZ[ebp_ F_g^_e__Z ke_^hZl_evgh Z 203. eblbc[ 204. nlhj MijZ`g_gb_Wlb Zlhfu bf_xl h^bgZdhu_ fZkku gh bo obfbq_kdb_ khcklZjZaebqguWlhh[tykgy_lkyl_fqlh m gbojZagu_aZjy^hu_ qbkeZZagZqblb dhebq_klhwe_dljhgh MijZ`g_gb_92 U 90Th + 2 He . 238234 41.90Th 91Pa + 1 e+ 0; 91Pa 92 U + 1 e+ 0 Ke_^hZl_evgh 234 23400 ~ 234234 00~j_amevlZl_^mojZkiZ^h2. MijZ`g_gb_Ld gmdehgu bf_xl fZkkm lh f_`^m gbfb ^_cklmxl kbeu]jZblZpbhggh]hijbly`_gby 55 205. AZ^Zqbij_^eZ]Z_fu_^eyihlhj_gbyb ijbqZkZonbabdb g_^_ex71. ey_dlhjZ a bf__fZ 206. [ 207. Zy 208. _Zy| =7] 209. | a | = (0,5 0,5) 2 + (2 5) 2 = 3.7ey_dlhjZ b bf__fZ 210. [ 211. by 212. _by_ ] 213. 77| b | = (4 1) 2 + (4 0) 2 = 5.ey_dlhjZ c bf__fZ 214. [ 215. cy 216. _cy_] 217. 77| c | = (6 4) 2 (1 1) 2 = 2.ey_dlhjZ d bf__fZ 218. 219. [ 220. dy 221. _dy_ ] 222. 7| d | = (3 6) 2 + (4 0) 2 = 5ey_dlhjZ e bf__fZ 223. 224. [ 225. ey 226. 7|ey_ ] 227. | e | = (0,5 0,5) 2 + (1 (4)) 2 = 3. 7 72. ax = 0, bx = | b | , cx = 0, dx = | d | .3. Z 228. A (0;2), B 229. [ 230. sx = 12 0 = 12, sy 231. _sx| = 12,7|sy| = 5; ] 232. | s | = (12 0) 2 + (3 2) 2 = 13.4. y B x AsAB = ( 4 ( 8)) + (3 ( 2)) 2 2 LZd dZd imlv g_ fh`_l ij_ukblvi_j_f_s_gbyfh^mevdhlhjh]h_klvgZbf_gvr__jZkklhygb_f_`^mgZqZevghcb dhg_qghclhqdZfbimlb 233. lhhgfh`_l[ulveb[hjZ_geb[h[hevr_i_j_f_s_gbyghgb dh_fkemqZ_g_f_gvr__]h5. Ijyfhebg_cguf jZghf_jguf ^b`_gb_f gZauZ_lky lZdh_^b`_gb_ ijb dhlhjhf aZ h^bgZdhu_ ijhf_`mldb j_f_gb l_ehkh_jrZ_l h^bgZdhu_ i_j_f_s_gby ^hev g_dhlhjhc hkb lZd dZd^b`_gb_ ijyfhebg_cgh_ 234. Ihwlhfm sx = vxt ]^_ vx ihklhyggZy 56 235. _ebqbgZ oZjZdl_jbamxsZy kdhjhklv i_j_f_s_gby Bkoh^y bamjZg_gbyo = o0 + sxihemqbfx = x0 + vxt.Zgh J_r_gb_6.vx fkx0 f x(t) = x0 + vxt x(t) = 3 + 5t.GZclbx(t). Hl_lx(t) = (3 + 5t 236. f hdaZe x7.xlxi XZghJ_r_gb_xi = 260 10tgZqZevgucfhf_glgZ[ex^_gbyxl = 100 + 8t xi = 260 10 0 = 260; xl = 100 + 8 0 = 100.fhf_glklj_qbxi = xl bebt = 100 + 8t. Hlkx^ZgZoh^bffhf_glj_f_gbklj_qbt = 20 c. x = 260 10 20 = 100 + 8 fGZclb xi, Hl_lxi = 260, xl = 100, t = 20 c, x fxl, t, x.8. Kh]eZkgh]jZnbdmiehl[uekims_ggb`_klhygdbgZf_ljhIh]jZnbdmhij_^_ebfo0 = 10; vx fk fko = 10 + 2t.ZghJ_r_gb_9.t=2c v v0 v v t 4,5 fk 2 k3 fkv= ; t1 = 1 = 1 =v fkv0 = 0 a= = 3 c;at 2 vv 2 t 2 v 2 t (4,5 fk )2 2 ktt a vv1 fk = 6,75 f 2 3 fk s= 1 = 1 2 = 1 =GZclbt1, s. Hl_l: t1 = 3 c, s = 6,75 f.2 2tv 2v77 7 77 7 at 2 7 at t 77 7 v +v10. s = v0 t += t v0 + = (v0 + (v0 + at )) = 0 t.7 7 77 77 7 22 227 7 a t 2 7 v v0 7 7(v v 0 )t 2 v 0 + v11. s = v0 t + ; a=; s = v0 t + = t; 7 7 7 772 72 77777 7 7 7 2 t 2t2( )(a , s ) = v v0 , v0 + v t = 1 (v , v0 ) + v 2 v02 (v0 , v ) = v v0 72 72 t 2 2 2 7 v v0a=7 .2sZgh J_r_gb_12.tx = 0,3 k 57 237. s fs 0,43 f 1,43 fk 0,3 kvkj == 2 s 2 0,43 f t 2,87 f/k. 0,3 k 2s a = 2 ; v = at = =GZclbvkj, v.Hl_lvkj fkv fk tt13. so[ = o[ ; sFd = cd = o[ = 3sh[. jZaZ[hevr_ 2 a ta t 2 3a t 2vkd = acdt = 3ah[t = 3vh[. jZaZ[hevr_ 2 2 2 eykdhjhklgh]h14.ebnlZ vx eyh[uqgh]hebnlZ0 tZgh J_r_gb_15.v0x = vx(0) = 10 + 0,5 fka fk2.K l_q_gb_f j_f_gb fh^mev _dlhjZ kdhjhklbvx(t) = 10 + 0,5tZlhfh[beyhajZklZ_llZddZdZ!b v00).GZclbv0x.Hl_lv0x fk16. Ihke_ m^ZjZ mkdhj_gb_ rZc[u gZijZe_gh ijhlb kdhjhklbDh]^Z kdhjhklv h[jZsZ_lkygmev mkdhj_gb_ lh`_ klZghblky (5 t ) fk 0 t 5;jZgufgmex | v x (t ) |= 0 fkt5.vx t58 238. 17. o = o0 + sx JZg__ [ueh ^hdZaZgh qlh ijb jZghmkdhj_gghf^b`_gbbk mkdhj_gb_fZo b gZqZevghckdhjhklvx v0x i_j_f_s_gb_jZghsx = v0xt + x ihwlhfmo = o0+ v0xt + x .a ta t 22Zgh J_r_gb_18.ax fk2vx(t) = v0x + axt = 0,1tfk2).v0x = 0 a t2 0,1 t 2x0 = 0x(t) = x0 + v0xt + x = = 0,05t2.GZclbvx(t), x(t). Hl_lv0x fk 22Zgh J_r_gb_19.|v_ dfq|vf| = ||v| |v|| ijb v vf beb |vf| = ||v| + |v||Z 239. |vhlg| = 0 ijb v vf.[ 240. |vhlg_ dfq Z) v vf b v vf |vf| = |40 df/q 0 df/q| = 241. |vhlg_ dfq = 40 df/q.] 242. |vhlg_ dfq [) v vf |vf| = |40 df/q 10 df/q| = 30 df/q.v vf |vf| = |40 df/q + 10 df/q| = 50 df/q. 243. v vf |vf_ _dfq dfq_ v vf |vf_ _dfq dfq_ dfq] 244. v vf |vf_ _dfq dfq_ dfqv vf |vf_ _dfq dfq_ dfqGZclbvf. Hl_l Z 245. dfq [ 246. dfq bebdfq 247. bebdfq[ 248. dfq bebdfq20. KdhjhklvdZl_jZhlghkbl_evgh[_j_]Zihl_q_gbxvd == vd + vl = 6vl a^_kvvd kdhjhklvdZl_jZhlghkbl_evghh^uvl kdhjhklv l_q_gby h^u hlghkbl_evgh [_j_]Z 249. kdhjhklv dZl_jZhlghkbl_evgh [_j_]Z ijhlb l_q_gby vd = vd vl = 4vl LZdbfh[jZahf d + = = 1,5. v 6 vd 4 m 3,87 10 3 d] d]f3 Fu b^bf qlh iehlghklv3 10 3 f 321. = =rZjbdZjZgZiehlghklbha^moZZke_^hZl_evghulZedbZxsZy VkbeZ ^_cklmxsZy gZ rZjbd jZgZ _]h kbe_ ly`_klb AgZqbl ihi_jhfm aZdhgm GvxlhgZ rZjbd hklZg_lkykhklhygbb ihdhy ld_]h hlimklbeb [_a gZqZevghc kdhjhklb bgZq_ [u hg jZghf_jgh bijyfhebg_cghi_j_f_sZeky 250. 22. Kh]eZkghlj_lv_fmaZdhgmGvxlhgZkbeu^_cklmxsb_gZrZjujZguKh]eZkghlhjhfmaZdhgmGvxlhgZbomkdhj_gbyjZgu 59 251. Zk = , ZZ =Hlkx^Z c = a j_Zevguo nbabq_kdboFFamaZ^ZqZo dh]^Z fZkku rZjh g_ jZgu gmex 252. fh^mev mkdhj_gby mcma a a mcklZevgh]h rZjZ g_ fh`_l jZgylvky gmex Hg fh`_l [ulv dZd[hevr_ lZd b f_gvr_ fh^mey mkdhj_gby Zexfbgb_h]h rZjZ qlhaZbkblebrvhlkhhlghr_gbyfZkkrZjh23. Ba nhjfmeu ^ey g0 ihemqZ_f GM3 = g 0 R3Ih^klZeyy 2nhjfmem^eygihemqZ_fg = 2g 0 R3.( R3 + h) 2= a1 ; L1 = ma1 ; L2 = ma 2 = ma1 = L 1 . v2v2 11124. a1 =; a1 =DZd mkdhj_gb_lZd b kbeZ^_cklmxsZy gZ lhjhc rZjbdjZaZr2r 222f_gvr_ZgZeh]bqguo_ebqbg^eylhjh]hrZjbdZ25. GZ ukhl_ h hlghkbl_evgh a_feb r = R3 + h; mapk = mg; 2 2v2g 0 R3g 0 R3= v= ( R3 + h) ( R3 + h) 2R3 + hZgh J_r_gb_26.R df 106 fhkihevam_fkynhjfmehc ihemq_gghc g0 fk2ij_^u^ms_caZ^Zq_h df 106 f2 g 0 R3 9,8 fk (6,4 10 6 f 253. 26,4 10 6 f + 3,6 10 6 fv=v== R3 + h fkGZclbv.Hl_lv fkvx, fk27. vx = gt. t, c Zgh J_r_gb_28.l d] p = mv = mgt.60 254. Ldv1 = v2 jZghmkdhj_ggh_^b`_gb_ 255. lht k p1 = p2 = p d]fk2 1 c d]fkv0 = 0t = 1cGZclbv. Hl_lp1 = p2 = p d]fk29. Ld m ihklhyggZy _ebqbgZ lh baf_g_gb_ bfimevkZ [m^_lhij_^_eylvky lhevdh baf_g_gb_f kdhjhklb Ih ]jZnbdm kf aZ^Zqm 256. b^ghqlh_kebt1 = t2lhb v1 = v2bagZqblp1 = p2.30.mkehbyo kh[h^gh]h iZ^_gby kdhjhklb h[hbo rZjbdh ex[hc fhf_gl j_f_gb [m^ml h^bgZdhu b ke_^hZl_evghhlghr_gb_ bo bfimevkh [m^_l aZbk_lv ebrv hl hlghr_gby bofZkk LZd dZd ih mkehbx h[t_fu h^bgZdhu hgh [m^_l jZgh f 8,9 10 3 d]f 3hlghr_gbxiehlghkl_cf_^bb Zexfbgby Z 2,7 10 3 d]f 3= 3,3.BlZdex[hc fhf_gl j_f_gb f_^guc rZjbd bf__l bfimevkijbf_jgh jZaZ[hevr_q_fZexfbgb_uc ^hklhedgh_gby31.1 2X ihke_klhedgh_gby 1 2 XZghJ_r_gb_v1x fk Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O):v2x fk v1x fk mv1x + mv2 x = mv1x + mv2 x v 2 x = v1x + v 2 x v1x = fk fk fk fkGZclbv. Hl_l v x fk 2 ^hklhedgh_gby32.12 X ihke_klhedgh_gby 1 2 XZghJ_r_gb_v1x fk Ih aZdhgm khojZg_gby bfimevkZ gZ hkv O):v2x fkmv1x + mv2 x = mv1x + mv x v x = v1x + v 2 x v1x = fk fk 257. fk 258. fk 2 2GZclbv.v1x = fk Hl_l v x fk 233.() mv 2 mv 2 m () 22mv1x mv2 x m 2E= += v1x + v 2 x ; E = 1x +22x= v1x + v 2 ; 2 2x 2 2 222 261 259. v1x + v2 x fk 260. 2 + fk 261. 2 = 0,05 f2k2; v1x + v22 fk 262. 2 + 2 22x+ fk 263. = 0,05 f k v1x + v2 x = v1x + v x E = E.22 22 22 2234. Ih ]jZnbdm hij_^_ey_f qlh L k b = =p11=Ex[Zy^jm]ZylhqdZbaf_gy_lkdhjhklvk lhc`_kZfhcqZklhlhcT 2c35. havf_f aZ t fhf_gl dh]^Z hldehg_gb_ kj_^g_c lhqdbkljmgujZghgmex=jZnbdg_]h^blky^ey^jm]bolhq_dkljmguldZfieblm^ZbohlebqgZhlZfieblm^ukj_^g_clhqdbeykj_^gbolhq_dkljmg ^jm]bo Zjnhgl_f[he__g_]h^blkylZddZdhgbbf_xlbgu_qZklhludhe_[Zgbc;ffWfF 36. GZ^h ^Z h^bgZdhuo dZf_jlhgZ jZkiheh`blv gZ g_dhlhjhfjZkklhygbb ^jm] hl ^jm]Z lZd qlh[u bo j_ahgZlhjgu_ ysbdb [uebh[jZs_gu ^jm] d ^jm]m ?keb l_i_jv m^Zjblv ih h^ghfm ba gbo bq_j_ag_dhlhjh_j_fyaZ]emrblvijbdhkgmrbkvjmdhcd g_fmlhfu mkeurbf amd hl lhjh]h dZf_jlhgZhkgh_ ^Zggh]h hiulZe_`blye_gb_amdhh]hj_ahgZgkZ37. Ihevamykv ]jZnbdhf hij_^_ey_f Z 264. ijb=p Zfieblm^ZmklZghbrboky dhe_[Zgbc [m^_l [hevr_ q_f ijb=p [ 265. qlh[uZfieblm^Z mklZghbrboky dhe_[Zgbc [ueZ fZdkbfZevghc dZq_ebgZ^hih^lZedbZlvk qZklhlhc=p 266. kh[kl_ggZy qZklhlZ dZq_e_cjZgZqZklhl_ugm`^Zxs_ckbeul_=pZgh:J_r_gb_38.l kf f mg 0,002 d] 9,8 fk 2m ] d] Fl = Ff; mg = BIl I = 4 10 2 Le 0,1 f =B = 4 10-2 Le =BlGZclbI. Hl_l: I = 4,9 A. = 4,9 A.39.^Zgghf kemqZ_ jhev p_gljhklj_fbl_evghc kbeu uihegy_lkbeZ k dhlhjhc fZ]gblgh_ ihe_ ^_cklm_l ^b`msbcky we_dljhgIhevamykvijZbehfe_hcjmdbhij_^_ey_fqlhwe_dljhge_l_edZf_jm lhqd_. 62 267. ZghJ_r_gb_40.v = 3 107 fk|_| = 1,6 10-19 Demv 2 mv Fpk = Ff; = B|_|v r =m = 9,1 10-31 d]= r B|e|B = 8,5 10-3 Le9,1 10 31 d] 3 10 7 fk = 2 10-2 f8,5 10 3 Le 1,6 10 -19 De =GZclbr.Hl_lr = 2 10-2 f41.j_amevlZl_jZkiZ^Z 14 C 14 N + -0 e .67113 Al+ 0 n 11 N + 2 He .27 124442.43. 107+ 410 5 Al+ 3+ 25 X 3 N + 2 He 74 7 + 4103+ 25 X = 0 n g_cljhg 1 63 268. EZ[hjZlhjgu_jZ[hlu EZ[hjZlhjgZyjZ[hlZBkke_^hZgb_jZghmkdhj_ggh]h^b`_gby[_agZqZevghckdhjhklbZjbZglP_evjZ[hlum[_^blvky jZghmkdhj_gghfoZjZdl_j_^b`_gby[jmkdZb hij_^_eblv_]hmkdhj_gb_b f]gh_ggmxkdhjhklv ^ZgghfZjbZgl_jZ[hlubkke_^mxloZjZdl_j^b`_gby[jmkdZih gZdehgghc iehkdhklb K ihfhsvx ijb[hjZ bah[jZ`_ggh]h gZjbkZ 269. mq_[gbdZ fh`gh baf_jylv fh^meb _dlhjhi_j_f_s_gbckh_jr_gguo[jmkdhfaZijhf_`mldbj_f_gbt1, t2 == 3t1,, tn = nt1hlkqbluZ_fuohlfhf_glZgZqZeZ^b`_gby?keb2t1, t3 =aZibkZlv^ey^Zgguofh^me_c_dlhjhi_j_f_s_gbcboujZ`_gbya (2t1 ) at 2 a (3t1 ) 2 2 at12 at 222 32 s1 = , s 2 = 2 === s1 , s3 = 3 ==s3 ,,22222 2 2at 2 a (nt1 )2 n 2sn = n == s1 ,lhfh`ghaZf_lblvke_^mxsmxaZdhghf_jghklv22 2?keb wlZ aZdhghf_jghklv uihegy_lky ^ey baf_j_gguojZ[hl_ s1 : s2 : s3 : : sn = 12 : 22 : 32 :: n2 = 1 : 4 : 9 :: n2.fh^me_c _dlhjh i_j_f_s_gbclh wlhb [m^_l ^hdZaZl_evklhf lh]hqlh ^b`_gb_ [jmkdZ ih gZdehgghc iehkdhklb yey_lkyjZghmkdhj_ggufIjbf_juiheg_gbyjZ[hlu.AZ^Zgb_Bkke_^hZgb_ oZjZdl_jZ ^b`_gby [jmkdZ ih gZdehgghciehkdhklb0,02 0,040,06 0,080,10 0,120,14 0,160,18 0,200,22 0,240,26 0,280,30t, c0sff 102126 146170 198227 1524 3650 658201 37uqbke_gby.s 2 3 ff7 ff15 ff 24 ff s1 1 ffs1 1 ff s1 1 ff 1 ffs s s = = 3, 3 == 7, 4 = = 15, 5 = = 24,s164 270. s 6 36 ff 50 ff 65 ff 82 ff 1 ff1 ff 1 ff 1 ffs s s == 36, 7 = = 50, 8 = = 65, 9 = =82,s1s1s1s1s10 102 ffs 11 126 ff 146 ff1 ff1 ff 1 ff ss== 102, = = 126, 12 == 146, 13 = s1 s1s1s1170 ff 198 ff 227 ff1 ff 1 ff 1 ffs s== 170, 14 == 198, 15 == 227.Hlkx^ZgZoh^bf s1s1s1 : s2 : s3 : s4 : s5 : s6 : s7 : s8 : s9 : s10 : s11 : s12 : s13 : s14 : s15 =WlZ aZdhghf_jghklv g_ hq_gv kbevgh hlebqZ_lky hl l_hj_lbq_kdhc= 1 : 3 : 7 : 15 : 24 : 36 : 50 : 65 : 82 : 102 : 126 : 146 : 170 : 198 : 227.aZdhghf_jghklb ^ey jZghmkdhj_ggh]h ^b`_gby LZdbf h[jZahffh`gh kqblZlv qlh ^b`_gb_ [jmkdZ ih gZdehgghc iehkdhklbyey_lkyjZghmkdhj_ggufAZ^Zgb_ Hij_^_e_gb_mkdhj_gby^b`_gby[jmkdZMkdhj_gb_[m^_fuqbkeylvihnhjfme_a = 2 .2s2 0,102 ftt10 = 0,2 c; s10 = 102 ff = 0,102 f; a1 = = 5,1 f/k2.(0,2 k) 22 0,227 ft15 = 0,3 c; s15 = 227 ff = 0,227 f; a1 = 5,04 f/k2.(0,3 k)2 a1 + a 2 5,1 fk 2 + 5,04 fk 2akj == fk2.AZ^Zgb_Hij_^_e_gb_ f]gh_gghc kdhjhklb [jmkdZjZagu_22fhf_glu j_f_gb b ihkljh_gb_ ]jZnbdZ aZbkbfhklb f]gh_gghckdhjhklbv hlj_f_gbt.AgZq_gb_f]gh_gghckdhjhklb[m^_fuqbkeylvihnhjfme_v = at.t = 0,1 c; v fk2 k fkt = 0,2 c; v fk2 k fkt = 0,3 c; v fk2 k fk=jZnbdaZbkbfhklbf]gh_gghckdhjhklbv hlj_f_gbt.65 271. v, fc t, chihegbl_evgh_ aZ^Zgb_ Ihkljh_gb_ ]jZnbdZ aZbkbfhklbdhhj^bgZlu x [jmkdZ hl j_f_gb t. x0 = 0, t0 = 0, xi(ti) = si, i =x, ff1,2,3,,15.ZjbZgl t, c P_ev jZ[hlu hij_^_eblv mkdhj_gb_ ^b`_gby rZjbdZ b _]hf]gh_ggmxkdhjhklvi_j_^m^Zjhfh pbebg^j b`_gb_ rZjbdZ ih gZdehgghfm `_eh[m yey_lkyjZghmkdhj_gguf ?keb fu hlimklbf [_a gZqZevghc kdhjhklbrZjbd b baf_jbf ijhc^_ggh_ bf jZkklhygb_ s ^h klhedgh_gby kpbebg^jhf b j_fy t hl gZqZeZ ^b`_gby ^h klhedgh_gby lh fufh`_fjZkkqblZlv_]hmkdhj_gb_ihnhjfme_a = 2 . 2sAgZymkdhj_gb_afufh`_fhij_^_eblvf]gh_ggmxkdhjhklvv ih tnhjfme_Ijbf_juiheg_gbyjZ[hlu. v = at. QbkehMkdhj_gb_j_fy F]gh_ggZy m^Zjh JZkklhygb_ ^b`_gbykdhjhklv f_ljhghfZ fk2s 2 sf a= nt, ct2 v = atfk 30,91,5 0,81,266 272. uqbke_gby. 2 0,9 f fk2; v fk2 k fk (1,5 k )2t = 0,5 c 3 = 1,5 c; a = EZ[hjZlhjgZyjZ[hlZ Baf_j_gb_mkdhj_gbykh[h^gh]hiZ^_gbyP_ev jZ[hlu baf_jblv mkdhj_gb_ kh[h^gh]h iZ^_gby kihfhsvxijb[hjZ^eybamq_gby^b`_gbyl_eKh[h^gh_ iZ^_gb_ l_eZ yey_lky jZghmkdhj_gguf ^b`_gb_f?keb fu hlimklbf [_a gZqZevghc kdhjhklb dZdhcgb[m^v ]jma gZmklZghd_hkh[h`^Z_faZ`bf 273. b baf_jbfijhc^_ggh_bfjZkklhygb_s b j_fy taZdhlhjh_ [ueh ijhc^_gh wlh jZkklhygb_ lh fu fh`_fjZkkqblZlvmkdhj_gb_kh[h^gh]hiZ^_gbyihnhjfme_g = 2 .2sIjbf_juiheg_gbyjZ[hlu.t j_fy Mkdhj_gb_kh[h^gh]h^b`_gbyt = Imlvsff Imlvsf iZ^_gbyg = 2s/t2fk2nT, cuqbke_gby.0,28 400 0,42 0,4 fn = 14; t = 14 0,02 c = 0,28 c; gwdki = (0,28 k )2fk2.g = |gwdki gl_hj _ _fk2 fk2_ fk2.g0,4 fk 29,8 fk 2 100% = 100% 4,1 %. g EZ[hjZlhjgZyjZ[hlZBkke_^hZgb_aZbkbfhklbi_jbh^Zb qZklhlukh[h^guodhe_[Zgbcgblygh]hfZylgbdZhl_]h^ebgu P_evjZ[hluuykgblvdZdaZbkyli_jbh^b qZklhlZkh[h^guodhe_[Zgbcgblygh]hfZylgbdZhl_]h^ebgu Ijbbaf_g_gbb^ebgugblygh]hfZylgbdZf_gy_lky_]hqZklhlZbi_jbh^^Zgghc jZ[hl_ fu ^he`gu hij_^_eblv wlm aZbkbfhklvI_jbh^ b qZklhlm hij_^_ey_f ke_^mxsbf h[jZahf HldehgbfrZjbdfZylgbdZhliheh`_gbyjZgh_kbygZg_[hevrmxZfieblm^mb aZk_q_f j_fy tl_q_gb_ dhlhjh]h fZylgbd kh_jrbl N .dhe_[Zgbc Lh]^Z i_jbh^ b Zfieblm^m fh`gh ihkqblZlv ihnhjfmeZf 67 274. t1 N T=, = = .Baf_jyy i_jbh^ b qZklhlm ijb jZaguo agZq_gbyo ^ebgu fZylgbdZN T tful_fkZfufihemqZ_faZbkbfhklvi_jbh^Zb qZklhluhl^ebguIjbf_juiheg_gbyjZ[hlu. hiulZ Nba_e1 2 3 45 lkf 5 20 45 80 125 N 3030 30 3030t, c 1327 40 5367 , =pT, c0,430,91,33 1,772,23Ba ^ZgguolZ[ebp_ fh`gh aZf_lblv lZdmx aZdhghf_jghklv q_f2,311,11 0,75 0,570,45[hevr_ ^ebgZ fZylgbdZ l_f [hevr_ i_jbh^ b f_gvr_ qZklhlZ bgZh[hjhlhihegbl_evgh_aZ^Zgb_.P_ev aZ^Zgby uykgblv dZdZy fZl_fZlbq_kdZy aZbkbfhklvkms_klm_lf_`^m^ebghcfZylgbdZb i_jbh^hf_]hdhe_[Zgbc T2T3T4 4 T523 5 T1T1T1 T1 l2 l3 l4 l 2 = 25=4 =9 = 16 l1 l1 l1 l1Ba ^ZgguolZ[ebp_ ohjhrh ijhkfZljbZ_lky kyav f_`^m i_jbh^hfdhe_[ZgbcfZylgbdZb _]h^ebghc]^_k fh`_lijbgbfZlvTk lk =T1b l1EZ[hjZlhjgZyjZ[hlZBamq_gb_ye_gbywe_dljhfZ]gblghcbg^mdpbbP_evjZ[hlubamqblvye_gb_we_dljhfZ]gblghcbg^mdpbbDZd ba_klgh ye_gb_ we_dljhfZ]gblghc bg^mdpbb aZdexqZ_lky hagbdgh_gbb we_dljbq_kdh]h lhdZaZfdgmlhf ijhh^gbd_ ijbbaf_g_gbb fZ]gblgh]h ihlhdZ ijhgbauZxs_]h hoZq_ggmxijhh^gbdhfiehsZ^vIjbf_juiheg_gbyjZ[hlu.1. K[hjdZmklZghdbjbkmq_[gbdZ 275. 2.i_jhfhiul_bg^mdpbhgguclhdhagbdZe dZlmrd_kemqZ_dh]^Z fZ]gbl ^b]Zeky hlghkbl_evgh dZlmrdb Ijb lhjfh`_gbbfZ]gblZ kbeZ bg^mdpbhggh]h lhdZ j_adh hajZklZeZ b iZ^ZeZ ^hgmeydh]^ZfZ]gblhklZgZebZekyihdhbeky 276. 68 277. 3. Baf_g_gb_ fZ]gblgh]h ihlhdZ yey_lky ijbqbghc hagbdgh_gbybg^mdpbhggh]hlhdZL_fZ]gblgucihlhdijhgbauZxsbcdZlmrdmf_gyekyf_kl_k bg^mdpbhgguflhdhfl_hj_fy^b`_gbyfZ]gblZ4. Bg^mdpbhgguc lhd hagbdZedZlmrd_ ijb baf_g_gbbfZ]gblgh]hihlhdZijhgbauZxs_]hwlmdZlmrdm5. Ijbijb[eb`_gbbfZ]gblZd dZlmrd_ fZ]gblguc ihlhd f_gyekyld fZ]gblguc ihlhd aZbkbl hl fh^mey _dlhjZ fZ]gblghc7bg^mdpbb B fh^mev wlh]h _dlhjZ g_ ihklhyg_g ld fZ]gblgh_ihe_ihklhyggh]hfZ]gblZg_h^ghjh^gh 278. 6. GZijZe_gb_ bg^mdpbhggh]h lhdZ [m^_l jZaebqguf ijbijb[eb`_gbbfZ]gblZd dZlmrd_b m^Ze_gbb_]hhlg__7. Q_f [hevr_ kdhjhklv ^b`_gby fZ]gblZ hlghkbl_evgh dZlmrdbl_f [hevr_ fZ]gblguc ihlhd Z ke_^hZl_evgh b agZq_gb_bg^mdpbhggh]hlhdZ8. K[hjdZmklZghdbjbkmq_[gbdZ 279. 9. Bg^mdpbhgguclhdhagbdZ_l kemqZyoZ 280. b 281. 10. FZ]gblgucihlhdf_gy_lky kemqZyoZ 282. b 283. 11. hagbdgh_gb_ we_dljbq_kdh]h lhdZfh^_eb ]_g_jZlhjZ jbkmq_[gbdZ 284. Bg^mdpbhgguclhdhagbdZ_l jZfd_jZsZxs_cky fZ]gblghf ihe_ ke_^klb_ baf_g_gby fZ]gblgh]h ihlhdZye_gb_we_dljhfZ]gblghcbg^mdpbb 285. EZ[hjZlhjgZyjZ[hlZ Bamq_gb_^_e_gbyy^_jmjZgZihnhlh]jZnbyflj_dh P_ev jZ[hlu m[_^blvkykijZ_^ebhklb aZdhgZ khojZg_gbybfimevkZgZijbf_j_^_e_gbyy^_jmjZgZIjbf_juiheg_gbyjZ[hlu.AZ^Zgb_Y^jhmjZgZijbaZoZl_g_cljhgZjZa^_ey_lkyijbf_jghgZ^_jZgu_qZklbdhlhju_gZauZxlkyhkdhedZfb^_e_gbyIjbwlhfhkdhedb jZae_lZxlkyijhlbhiheh`gu_ klhjhgu Wlh fh`ghh[tykgblv gZ hkgh_ aZdhgZ khojZg_gby bfimevkZ Bfimevk y^jZmjZgZ ^h aZoZlZ g_cljhgZ ijZdlbq_kdb jZ_g gmex Ijb aZoZl_g_cljhgZy^jhihemqZyhlg_]hg_dhlhjucbfimevkjZkdZeuZ_lkygZ^_ jZae_lZxsboky qZklb fZkkZfb m1 b m2 ?keb aZibkZlv aZdhg77khojZg_gby bfimevkZ 0 = m1v1 + m2 v lh kjZam b^gh qlh kdhjhklb h[jZahZrbokyhkdhedhijhlbhiheh`ghgZijZe_gu^jm]^jm]mb 2ke_^hZl_evghqZklbpujZae_lZxlky ijhlbhiheh`gu_klhjhguAZ^Zgb_ . 92 U + 0 n 56 Ba + Z X + 2 0 n kbem aZdhgZ khojZg_gbyaZjy^ZaZibr_f Z + 2 Hlkx^ZihemqZ_fZ IhlZ[ebp_BF_g^_e__Zhij_^_ey_fqlhwlhy^jhdjbilhgZ 69 286. EZ[hjZlhjgZyjZ[hlZ Bamq_gb_lj_dhaZjy`_gguoqZklbpih ]hlhufnhlh]jZnbyf P_evjZ[hluh[tykgbloZjZdl_j^b`_gbyaZjy`_gguoqZklbpIjbf_juiheg_gbyjZ[hlu.AZ^Zgb_Lj_db qZklbp ^b`msbokyfZ]gblghf ihe_bah[jZ`_gugZjbkmq_[gbdZldgZwlbonhlh]jZnbyoboljZ_dlhjbbdjbhebg_cguAZ^Zgb_Z 287. qZklbpu ^b]Zebkv ke_Z gZijZh [ 288. H^bgZdhZy^ebgZ lj_dh qZklbp ]hhjbl h lhf qlh hgb bf_eb h^bgZdhmxwg_j]bx 289. LhesbgZ lj_dZ mlhesZ_lky aZ kq_l lh]h qlhmf_gvrZeZkvkdhjhklvbaaZklhedgh_gbck qZklbpZfbkj_^uAZ^Zgb_Z 290. JZ^bmk djbbagu f_gyeky aZ kq_l lh]h qlhmf_gvrZeZkv kdhjhklv baaZ klhedgh_gbc k fhe_dmeZfb h^u [ 291. QZklbpu ^b]Zebkv kijZZ gZe_h baaZ lh]h qlh lhesbgZ lj_dhkijZZgZe_hm_ebqbZ_lkyAZ^Zgb_Z 292. We_dljhg ihklhyggh l_jye khx kdhjhklv aZ kq_lkhm^Zj_gbc k qZklbpZfb kj_^u b ihwlhfm lj_d bf__l nhjfmkibjZeb[ 293. We_dljhg^b]Zeky gZijZe_gbbk]ms_gbykibjZebihmdZaZgghc ur_ ijbqbg_ 294. Lj_d gZ jbk^ebgg__ ihlhfm qlhhg f_gvr_ckl_i_gbaZbfh^_cklm_lk kj_^hc70