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Unformatted text preview: (flint? _ ' 13.170 ' DIAMETER 0F ‘ BALLspzza'n /’ ‘\ ”A: 3 9t [3 V AHE‘R IMPACT‘OB‘ 'lume u ‘ , DllECHON =o.q JED—F : ,_ I - “L .1 . .1 (M e ‘ C m Us B—a—A V ‘ GWEN: an smce Ué \s N THe sc-meea-tou AND IN‘TIALV€LOC'TY‘U°=(5m/5 LAssong No FatC‘ruoNnge COMMON e: at: TAN6€NT B€TW€€N A AND B AT \MPACT ‘ MUST BE PAZALLEL To THE 34mm ‘7 B ' THU: . Home To N E 3 we. \0 TAN e: (:1) gs wuseeveg _‘ ‘0 musmso": w e= N (53.77am (man 363: 4 L _ o | __ , 1 UR e—‘Ioo [Ub— CQEFE QE 253113111051 (fl n-bsggcnoN - A K; / y. (Ucos 30°39. =Uv1 ‘ 1 E . #— 6m. —~l (ISWOS3dXORT—‘Um Um=l .3 (NCOUSEEXATION 0F floHeNTUH m g (m) mcecnou / // \ \ng) 1 . I \/ x?! V“ 0A Q05 9 +W‘We)n: NOAH W‘Ué / / ”v1 Q E . (5)2105 10.04H- o =ng 1n + on: / T (0303: L014t=¢mm (036) m B I (figllm . 1 c zeurwe vewcmgs «a :56 n mgggggtx} ¥ 1 6:01 Mensa—(trawv vet-mm ‘ d ' V g.o?.4:_—o)(om= ug-(UMM £73 ware 0' IN Teens oF x AND I (HQ. ' ZU- =(.o 4 (m -‘= .' Z' S M 13.169 (MIA; Um'cos 30°— ugsm 30° - N ‘ (0,230 =at.e,<n(msao°3— (7. sXsm 30'") =é BAgLTH BOWN WW“ ‘ E ‘ VGLOClTY 1: AS (Mpg: UV1$1N3OQ+UgCOS 30° 0 snow. BALI- (03 0—— (Luemcsw 30°)+(1-53(cosao\ BEBOUNBS (N A _ blEGCTtoN . MOTION OF A Puma-n.6- (02mm AT 03 , PABMLE L To 0A kg: «30 Huh *2 4391/2" _N_Q: ° coecr-‘mem- or L3=LZ +(lz.34o mlsSt 4181 W/s‘\€. lesrrrunou e ' Tmsroaercu-E POINTB (33:031 Between THE BALL 0: [1+ (2.34OtB-(q.8\/z)’cs 'AND THE WALL ‘ £32706 W ' o , ¥=¥°+®Dob ’ I u- .b Sig/e?— = angels: - 'k.= O +Ga.3741: ° \LB:(6313,74)(:EB3 [email protected]).3—l4 m’5)(’l-’ - e: 2°'7°5 ' 13:14.45 m ‘1': 45°— 10.1052 24,2qs° ON .oF n i m. mtbl ho»;u:me=~u‘sm¢ cam Trr o m w 3 aoccosem‘ru'wsu DIVIDING, TANe =TAND€ gm}; 7.0.7053 1 ‘ A: [$.94 WI .- e v 9‘ TAN 24.319433 » ’ h cl: XB— L1 CoT60°== 15114 m 186 13.175 was; 13.175 continued MA=MB=15£3 run—mm? (b) e_=___1 BLOCK B 15 zeTozNe—D To PoswwNCD 03= —U$mls‘ 5:0 WITH A. venom-r? or: sw/s-v $1Nce‘ €N€1LGY No FRICTION 1‘5 szeeveb AND 1H1>Acr$ BLOCK rA wmcu (n e=1 15 AT mes-r. 1N T1+€ IMPACT TOTAL HOHGNTOH (238-10 15 cousezveD AND PHASE: (5 .Repemeu 1 \mrH THE VELocrnes 01: A ANDB wretwuceb. THUS ”JA"= sm/s—e A111: log: 0 51Mce T116121; 1s No 132101014. THesC vecocme‘s Am: THE FINN. VELOQT1€$ OF A AND (5 2:1 Mpf‘Eswfls» gig ‘ fichns A AND 3 A25 QETUZNED 1-0 Pos'nou (D w1TH T111: SAME YeLOCtTY OF 7.5 M/s - 511105 ”11:116.? 15 aousetv'ta meme 15 No AmeouAl- IMPACT AND 12mm (1DMAX1H0M DEFLECTtoN OF THE SPEING (D)F1Ng1vg1_ogrr; QF— 2.1.06.1: A____ 1 0" 0A= Smls E'E= E ;M + CONSERVthoN OF TOTAL MOMEMOH .— l I 1 1 Wm THE spews 51.01195 BLOCK E) DowN AND I 5‘ +0 = «3;: 105' U\ A AND 13 SEDAQATC wrm A QONT\N01MG- wm1 Q51 31mg 3151;391:155 1 (”A‘03\Q =1 (Us-UA\ 65—01 e— 02, ~13» (11 ADD1NG (0 AND (1) S:_'_____C1+€\:_ Us '2. SOBTQMLTKNG (7.3 FROM 10 5g123 'mA_mE,—1 5 119a \N\T\A\_\.‘( UAa¢mfs U 0 11,505,145: 0.5 :1 8:1 05- 51m lug? o 3.9 03 2.5’w1/5 071' =25 1m/s InEACT SEE PHASE— I of fins 13.175” 2:1 AFreP. 1141:ch UA': o Uézsts (00 QQNSG‘IZXATIONU 01:12:11: "62 6? 0mm Q «J- .. rue—51MB ._ ‘ SWISAWN—O 4“ ,_.._...l A__ ; B - 1 kx m_ .1— - It: EON/1M ........ HAXMUH DCFL€C_ 191% KM, 0E. . g :22 3. 5 WOBKT [HID CMgDG" — 11121”ka )= L (1391331511151 1: 871511" n)‘MA1 N‘- X37941“ T1: 0 V1=—EQ(MAY\-= @o)(XMAX)l T: o 01-5 J-juq’x HKW‘B‘SAX T+V= T1+V1 1875+ o— o + 401me U1 7.: ——|— 33803 (XMM)- (3 3\(1¢!L91(q81..\¥ 63-1 Lung—0 683M <T,+u1_ =12. __Z BOTH A AND B HAVE THE SAME‘ veioq'r‘r 18.15— 401LHM— 4414$XMM=o 1N1T1ALLY AT 0? Z 5 W‘ /5 X11150 6me a? T1105 T1= 11111111111111=1uvzswswz 1 MMe RETURN OF B To ”om—“3“ (D BEFORE q \( IMPACT mun-1 A T: 375 T 1:0 T10 U11— +1931XMM1 ‘11: 31““ b . AT X.—_ Xqu T1: 0 V=L19LXMH=4OMAX 112 Tun—Kw; <1375+o 4018,.“ 1‘: EW‘EOB: (0 75103111: .“(401 0177121 (4.4145110. 1:15477— 2.190: 13.113 0 +6173 (0-15) 0E, UP;— 41611 M/s» €=o 1111.17048‘1“ - AFTER 11/19th 541 A AT P051110fl© EELATlXE X€LOC111€§ + (o —o.3(e\—\UA"7 —* (4.191 o)(1\-— 0 02;" m (CONTINOa) GNEW .' ' . THREE SPHERESUEHCH arm» in. ' AIM/D 5 ME cowvecrrp Br YNEXTEA/SIBL'E coRD WHICH IS smug c STRIK£$ 3 65 5mm WITH PER FEcTI-Y ELHSTICWPMT. FIND: (a) VELOCITY or EACH 5mm: PrP/‘ER CORD EcoMEs T/wr. . Cb) thcnozv 5F NIT/AL k-E. «F ’"D.'_" E_':_° ‘1’” 9:1 __ _ _ __ __ LosTWIfEN (4RD BECDHES MOT. Conlsmvn'uow oF ANGULNJ mom-mum A3001‘ 0 (a) 3’ WWW/WW 0F'VELOCI7IES JINC‘E Vernal: Passts 'rmaouéH o, H0:0, 0? Pan orc Min 3 - - ' ‘ t b Can/5.0FM0MEA/TUH: H ‘..n>"mAQ'A +163¥mbl£ +-'_§CX’"‘c1/£;—0 § 360-k3 SPACE VEHICLE wml 1%.:‘(450095' ; AS IT Passes THRweH O, EwasIVE cflnfieas :EPMUTE n‘ \ mrqs pnms Macks), 5(120 k3), AND enema). ; smanv M'TER, THE Posmcws 0F TH: 3 PM‘IS ARE Aozugflzmemm), B(/30m,39bm,972m), C(—II/9m,-zeam,r7an). 2 VELomTY or B )5 .1234 lion/s); +030 m); $2.913) 5, x— COMP of V5: ocnr or c [5 cue)“: - Ram/5. ~-’ .— o e c - - . .. @I G.» O =, G. 6... my:4yly+.mry’ USING :Dc‘leRmeAA/T FDRM- i _ ~. M «W 1,- ,mvv- 0 C l) _ Lab :1! [—35 g *0 . ’"—c ~I 4{+'V,=Vo ( H —_- 50 72 72 we +120 190345172 +Iw-ILH-1fif76 =0 $- 6. 1: NERGY PERFECTLY ELASTIC IMPACT : ‘ (WAWAVA), I50 330.660 416(UQ,(1Q ii imag‘:i.m'v;"+ {WW} _ 15-30721): (2) 500mm; 70 ztno Tm; coEFr, opgléllsywa hIYIDINGBYéo: Sewn-«E (I): ganja)“, “13‘: 4&3" {UBTRALT (2.): 2%”. = 44:0 coRQ‘ES Pan/95 To INITIA-L coMDITmA/S A-MD SHOULD BE ELmuvnWD. THE? EFO'RE 0‘0 < ' 72(0199'6 «9(a)? ~ mam“?—azomrc)t _ "29(1); 2, -_- o “weak—72m); +5‘h0x/o’-207.3£ x/a’+ #31 (flag: 0 f __ ® 72 (1%)3— 72(5); +0 — 452(1Q)3-/03.sam°’= o - FW (1)" ’U; : 1):) ‘ EC. 0'9, HFT’EQ REDuchoA/s '. f 1“: 0 ‘ 'BECOMES—M (Viv),- 7051); "12(1’2),g ~2‘r("E)J :- 1650 (1) WW 8 B W“ 1 33"“ 9°” " -(”71)a+~rc%+e are). = we ('2) '~ ‘ . . NEXTENSIflerC‘DI‘fiPOA/Eur (18:); UV (1531‘ 6(1&) = N90 (3) J ,m-g- 0F 35 ALONG Prb Musr 3 ”8/” BE EGUA-L To ya. CONS. or MOMEMTum .- Myorlmy; {.myi/A fir} com); o: Zmfl S'm60'- «103/3 5m 30' ) I 15/ :' 1W0}. C3 4 C N E12 wmom m: LINER-K MoM'EA/TUH , Mil/‘0 :Mng’k+mflalfa+mcyc 360060 !)= solar/aw(mmmwgynwm; 4 sag-+5405,» leaf-IZoé'rNcyé *(VEXE) _ , ENUATIIJC» we com: 0F n+2 um ‘/(_-cTo.i-‘s MD lWIpNéBY 60: : ® NHL-r 300 —560 :0 (U701: gony, (‘0‘ " 9 (ayes!) ”933:0 (Va)4=—660-3(u33 (s) , 0 (”is z +1320 ”(11052700 (fin); 1380- 301533 (a) 5U65711’0‘rm6 WOMH), (rug/~71; (2) mm (a); " ”8° *3 (”2)? * 9(’6o)+ 60%); = 2150 (Ha =930 ”A ’ 660 '30)?» "6036(112); :l‘f‘lD (U5):=—2991%' Sufism-rum” F0? (1.1;)5 A/vD ('VEJQNWOD/mpas): (”742, = -660 ~3(—2#o) = 6011/4 (1702-- I380 —3(3ao) - B‘iOM/s .R EcrHun/Cv FKoM(L+)TH4r(1J,1)x=.60 m/5, "/5 mm: 26: (60.0 M/5)_i +(50.o m15)o£+(3?ol,€)jv “ 1r .— xm(o.s)+("2'93'11;)(v3/z) 412,: Wk '03: 0.25003 3:0.zsogflé6 ‘ CMRYING INTO (3)," 17% = g J3‘(o,250 15):.- 0-866 1;; B EEO-250% 5. ‘ I u .. ‘ 20- 7W5. 1’;- fawn/a mfcfiéuz 0,0, - , =?‘mv‘.’fl°+o‘?6.‘ 15“” _5_ .zsqgma + 0.8tw6aaaofi + . (0:257) VJSI‘ME— o. 3550,13:an 12:0me 4.215; , h C D ” '= war-=91; u; 13,70, %:0.401%T’3~9 4 D (0W - T :441'11” m 0 2 b ' 5(NCE 'EQ.(I) was N07 0561) m OUR sow-now, : W1T+ZLWWZ+ 144.411: WE cm; 05? IT To <++Ea< ”we fiNsw‘E'R. suesT/ru‘rvuz; T‘H—e VALUES OBTH-INED Fo?’_ «pi >(W15’, ("Up “lb (“/35 INTO THE LE'FT' HAND MEMBER 07" EQ-(I),w1= 037m»! 340- 9(60)-I2/3so)-u(-zuo)_- 340 4er - 3760+ 5760 ~— /650‘ 0* .- 1" (0.150%)‘+;—(0.4013q1fa)‘+ gmm : #4110375”? ~ ' r l- I I ICE. LOST: 7o"- hm: é an(l—0.275)Ja_ ‘2' :7. my:— fRncr/M 0F k-£._L/JST = 3- ‘ GIVEN: BBLL H mm BAtL 13> ‘ wITH v0— (aft/519M577 C 7HENO sun: or may: M A (wtrzea: 66in.) H “A =—- , mp, WW (:1) VELucmEs OFBHND C Cb) BISTmI/cr c WHEPE’ BALL c H415 SIDE _——.—.—_—-—g.——— con/snmwon/ emu/EM MoMErJTuM GIVEN! TWO $HA~LL IDENTICHL SPf-‘ERES A MM) 3 MM _2 I: m1);,_d£+m(qf5) i +m(v‘27;)+nn4/‘ 4 CW'VEC-TED 5V 5 c0RD 0F LENGTH 2C: 600”“ ENunTWé coE’FEo 7— mm Vic'roQSI ILIDEONA rroelzonL,FkIcno/I/L1=ss SURFHC'E ® 4447- 461(0‘5lfrm4/ (41-8) {—U'" flagm’ (I) WHM'LLY TH'EY Ro‘furrE pun-u gamma/5 H.509, __ 1; J '7 fl (2? 6, AW!) G MOVES WITH 3": 1ft. . AVFTEQ COLD @ - 'm A +( 5) (”7‘93" -77,q '5 6265.?) BREAKS; SMEQES MOVE Mou& PAT‘h‘S «1/ TH k = 6/ ousEeI/ATIoN 0F MG. Non I/Tu ou‘i Co I 5(30m)v-_'——(66m)1f +(7z.5'i'vt-)(v3)g+c0c 330(12): ~66(5.76)+ (71 5X5, 76) + 0% fl? arc- —.322 56 (1775 E (3) CoNsEeVmIorJ 0F EVER GY m _ imv‘:émv‘+lm[(va)" KVQHL11+ WU”: Imam/£3 67m MULTIPLYWG an”, MD suserTI/TWG to”;- ‘1’17’Slhfi‘W7 Mtg; 1931/2173) £17,457; VALUES AND 3013) :[2 1i “30” (0' >76 /z- 1f 76 «r %¢:_5,5Mf_ ,f ((2)’= ( )+( c +(5. )+ c 5/117 IT": Dzqué' 6V2: vcnzvfime): 0 1f: 6.31.64? M7746: 6-668: 7,32 m ca‘r‘IELD5c; 7770773135733 WERCFoRE, 11;: 6+I.68= 7.68 «r- 765775—33 '4‘ me (I) (via) = er-Zb9: Hz 171651776245,er m2 3:720:751637- <2] N 59 EDS 45,11; M191!” 5(b) DIST/Wu"? d ___B)'__.~_.___\___.___ r: vfi ION OFLINEHR MOMENTUM Barons BQEAK: L: «230175 40:23:11}; AFTEK Blatan- SETTING L: La MID rmJnTWG coEFr': 0F UNITVEC‘MES' E33; 7—7”+7%Tv55: zovf (0 we) C(269)"327—.$'6 fi“+\7%‘ f3: 1’5: RT”; (2‘) (SEE FIGURE OF P0209. 14,53) 5vas7n‘3re r041)“ lung). W 14'54 QIV‘EN' BALLA HITS B err/ V {ma/5)}, _ 15+ 1, 3321; ' 1, :EH (3) 7773M; 1mm; HIT; SIDE HTc: 98in I07?) _U':(96f'+/é)_g I #5 7% or ” z " FIND:(¢OU MU>_ ,(bimlsmic: a, 1760319er 15%;2 L717 VB=¥VD (q; _— ._ _ J ._ _ __ _.._ ICONS' HTIUN 0? ANGULR'R HoMENT‘oM BEFORE 32mm (7,)”: 2m: (5: 2'm(0,3m)(12rad/:):m(z.16) lA’FTER 8REAK: HG: H= mug) d- mdfiflu’: 1713115 5?TTIN6#G=(HG):,21ndtr:m(2.lb) «74:1,03 (y) , v 170;! wars 15mm; mam T: 1(m)v‘+— . (2m)(cé) 0:}?!1}; z7—4n(0:3x)2)z= m(V;z+/Z. 96) F 1. 1. RECPLudd-(3)MDC4)‘ 7—_2_1nvl(l7+#fl)_725mv‘ 377mg, 7-70. 7250;: 0231276 1/; -I. 740 m/s mum-156:1? IILWD)‘Z%?m/s -RDHC‘I): 1r: Zqusmo): H.610m/, “rt-5L8? 1);:qu '1" 37,20!t/53l ‘ W1 (5) 4:£%-0.750m y FROM (I) Am)( (;z) W ye-(VQL‘IMM (5.701%)_a+(7,zo£/)j ,' (.03 1r:l£/70m/5,U 1%:2fi7m/5; 155:76lm/s ‘ ’2 Moo-£17515}? , ' <3 (b) DISTANcE d= 0,750,, _ 750mm ‘ Elma). (a— 72 .s)7.20= 10.0 _:a 725M? a=7‘I.o;n. 4 414171.:- ~M1§a+m(vg) L+m(’U‘5 913an (D 411%: Mm) +IMII («7,9 2/5- 9,66— 570 {7’6 0) 5,} o: o—vmw‘wag (153%: 0 (2) coNsERV/ITION oFANGUMR MOMENW A9007 com/I531) +3 (ao‘m)1T:—4v; + (72. Sm X05) .7 r; 17‘ SUBSTITvT/NG GIVEN ‘DHTA map USING-E0 (2): 300597;) 3- at}; +72 5 «7,, + 75/76 93/5) (a- 72 5%): 10,6 (3) NsEthnon 0F EHEKGY zlrm'tfo :- 1m 031-431.”. K’V‘BV'i-(Vfily l-l-z‘umtrc fDNID/Nc. ewm MULTIPLVWG- 6Y2 mMsflrdT/Uéi' 05)": 1144530) +17 "r8 G) "251' ‘ .3! .312: 3&4 in: ‘61:: 3:, z ‘3“; *1, "I‘ . ...
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