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Ch 3C Notes pdf - 9r€sm¥a1n oS‘(clans Sec 3 Jm 3.3 l...

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Unformatted text preview: 9r€sm¥a1n oS‘ (clans: Sec. 3.! Jm 3.3 l. Vcdvr 1 has man-'4-ucle anc‘ ai'rechI'on 2. Pod-hon “chat 7‘. ; Tm] :s assumal k Le a} oriau‘n. Med .‘5 oi (x,y). The Ved-or {Nah/J": *0 (Xd). ‘lou can “fink 0“ .I? a; 593C;;y:n5 um 906330“ 09 n. Pain-h. 1: (1.1) 3. Nohhon QI- ved'or ? on} vcd'vr in x AI‘I‘EL‘HOH 'r' x? + A - , - Y3 : um} Veu‘vr {A Y APrLc-h‘on m>1~> :3 (:) ,; x cm; ‘1 May La Sue-Hons of Ema 4. Vulgar AJlihon : Tail +0 Hem! Md—qu 51:3; F; so ““14 HS «tail a :5 at a ‘5 Law; Tk¢n 1" -5 _. r. + r: IS a ‘ILC‘LOP all-mun 1' - l ‘ I $P°M fl 5 +Rll *0 P2" 1'1qu 5. Comg o nenh Lulu : (g) . ’K '5 +L“ 3‘ Companew“ DC 1-". ’3 "5 'H“ a ComponevA a: F Ul) You can “Au-shad MMPORBNB I." 41"“; of vquor QJJA‘LBH. W55! 1"" mul‘Hr‘Y A . X" '5 a veJor a? ‘enfl-Hn x ?n 4L: 4 ‘ . a. VedD'H'] a SCAKQI A ‘ .l. 1, Luz-hon you 303 a. Vflc+or ‘2' -J |-‘ a, . veg or a? lena‘Ha y [n +Lxe J Amen-Hon -H\a.4 Fol/43 in Ail-“ham o? i: Ne». A V£c+or is 5 +imu ‘k‘I —u 4 A as l, -b xi ‘ + '\ 0.5 r ’F ‘ Y3 r XL ya (4'an ° SI“. as . r«?+?.. "'3 ) XI: 5 fine; (C) GGOMELH‘CQ‘V) +Le cowonerd‘s 09 a vu+0f are +L|¢ vu‘l-Oris . 41‘ S. HoriioM-a‘ Wmec on Mmeoneyfi-t DH)? perpenibu‘ou gram heat! 0: var, r +0 lnofiion’ml axis Verhca‘ OoMponen‘t '. DPOP Perpendkulal‘ SProm [mud Of ved-or {'0 VEchal axis Vresew‘aMon as [has 3 Sta. 3.] *0 3-3 H—x—bi 1.. Veal-or Scum-ac“ on Same lien as I‘M‘ AuMLu SuL+rac1>Pont a-L = C means 5 is “a: V41“ 'Hml navy} Le QJJGJ 40L _. _‘ * +0 obi’m‘n 0;. £=r1~n \y _. 4‘ C us “he vzd-or 70.1 “J4 *0 F3. *0 8d- '1; "’ So a + E‘ _, " " 1 r2 '3 ‘ "z or c = q—F,‘ 8. Displacemenf umJ Velocih’ “ Use. a; V¢c+0r no’tadn‘on MGM” “”0 J.‘mgns4‘onql Mo’n‘on abucLHOM 'an Same ‘3‘ $9..." as one Jmensronal WA £“’"‘H°“s' Two Dimensions AX=X‘-X; B'fi-r’; 7 AK mes 1: -§ - Ar A Van: E v...“ is a. Vader “n44 gun‘nh in “.5 4"“;an 9? Al". 5‘ v: [I‘M E = éi‘. 4 50:40 4t “ A: = 4"" dd: it alt ‘(ou bur-'43 V - V, '1: + V, j = L‘: + ELL; at dt 50 x “Mfonew‘ u? who}, Vs‘ J_x. a“. y componan“ Dc V'rlN-Hy 'y ‘ 3% Pr33en‘hxl'ion cg {ACOSI S‘C- 3-‘ +0 3'3 ‘3- 9. Aldehyde Mdlnoé {or chvloAing velocfln/ ( :2) “new Afgguewhcde, eac‘n Componen“ +0 3d: 7. “ Ix V = vi = r- m ( ) art no. Stand-rial” , us At “’0 :m {n l-‘M “-00 fifised 4'0 ‘HAL chin-“5 ‘H‘a‘jec‘bry. V 1‘5 441: ins4on+aneous VClW-H‘j- V b +an3en’t +0 “we hajerJ'oI-y am! [CH 3 :n5+an+aml0\l$ SPuJ. _; , He J-ZSP‘ncgmgn+ Vtciof 5r LabOMCS a 3* i 4. ea. 11- Kala-\vionénlp 593an 3 mm! [+5 componeak V,‘ am! V v ul. A A {I V:\/KL+\/Ya "v IVI= leng’rk 09 7: SpeeJ = ./ (3+ v,’ 9 , v vi 6: q - Anal: V Make; tutu" X ax-‘s = At‘d'Qn V: [For any veA‘m-I |F\= ,Ix‘vy‘ vLu-e x ““1 y are comgonenJrs o? F’] :2. Dot Vroclud (Scalar 1’ro49cé) I; a owl B an: veal-org “new .. 6: an ’1 Leiween a.t=]allElCo$6 M Ve§+orsaqnclv REF .‘5 aojculcd-EJ L2.) aclJing "0:10:35 03; Corresponulu‘na componen-Ls. _. al 4 L _. 0.: (2:) 5= (b2) 4.1:: a.L,+qILz+q3L3 = a Scalar a b, No+¢ : ,1? a and I? are non-zero vednrs ‘Hflen 2-1: =O—> 53L? Vrbuth-‘on 0‘ {Am : Sec- 3“ +0 3.3 ‘4' - 53. Afllica-hon oi :19" Prkoct A Pu-ln‘dc Move, along Hue Padl- shalom .9 Posihon vador r anal velocH-Y vedar 7 are ska-4m gar seledeJ L‘Mes. I? You wan+ 4-0 Know wkcn HM par’r-‘cl: n‘s dosed +0 or {at-a, you can +aKe vaa-A‘l'aae o: a ralaAu‘onsL‘rp bah-Jun F and \7 Mad [molds a4 44W". 0? closed appmadn. The Trasukry $3a3l‘am swag e545 +La+ Q r‘J. v ad fine 09 doses“ Narmada. So) use A -O r . V :0 4'0 sa‘ve ¥or lime o? closes“ approa. ‘4. Amkerafion , Ve‘oci'l-y and Pos'J-fon - SAM: 0m. D7M¢n$§nm\ CASP— E Pram-taken 05; $493.5 : Su- 3.\ h 3.3 '5‘ L5- A‘athch Me'HnoJ gr codcu‘ana accduakon (ad Gin» V.- (VX) yov Q“! 7; 5‘, LWu-enhwlina cock wmponeu‘ u» am" :3 X 4 ' {y} 70" {3.34 “- Ba calcultflina Hm 5mg Aviva-“v: a? wok a2 LOMf onen’c . a 4 lb, Tamaur" amJ Normal Confounh OS? Amalcrcd'ion Smack-“08 H’ is convenind *0 consiglgr JAM. uamponam‘ a? 3: ‘H‘OA is Parallel +0 Hat. +m3ec’mry (0.”) ant! Hag MMPOIIQIA" a? 2 +1.“; .3 eefpevmhcular +0 We “army (a) indeed a? koamw Mme“ Q, “4 Mn. prond' “1' 11‘: components a.” and 11* have kasrml mean;n9_ “”4 N041. : .. 4 (if ”'7‘, o» a anJ a”. are compo-newts 09 a. «y l —. Shane 01/ aural V are ‘30an "nnaen‘ +0 Ha: Jrrujcdora ) a.” Poinh in ‘qu SAM: cl Fred-Con as v . +r¢5u+onl . a” {s Hue 99¢" a? a: 44m.“ dag-A3 es ‘Hw. eafhde's SpeeJ ad- “5 +1“?— 90"; °$ a 'Hna'l- (Jonas; 3": chr8c‘w‘on (Makes Hae Pad-Cele +um) 1'1. Acuhrakon in Cu'raular Make“ 509905} an o‘o‘yd l’rrawds ok a circular PGH“ ad- aonfl'awl- spceJ. The magmhl; a: V f: con-S'bmln Lo‘l’ 4+: Al‘l‘lfA'u‘on in Wk-‘rJA V fOM‘B cons‘hlnHy _. dnanaes. Since v is changing) “new {5 an accelera+.‘on even “awglq Mme, speeJ {s cons‘hxn‘l’. fl Consiatr ‘7: “an; ‘7; , \7; is “A; valocdy a": +IAL 3 object a.“ a hm: 5: just ag'l-cr in§+.‘al {4045 Z. ‘7. a .. .. ‘ 4 ' The. diagram svgguh ‘Hmn‘ AV = V; -\r‘ 90m 4 Jrowau'cl .H‘e cen+er 0‘ .1—L‘e circle. In god) accdera’cwn (n uncle“- Mo‘l’l‘on {S Jn-ccjrecl +oware‘ Mae LEvA’er 09 HA; o'rcle. chapk-u 3- Mal-ion .‘n a Mane, Vechu- 0.139.er is oseA +0 Jud N;+L\ veloci ved'or (buamhhes. 3-! Average Ma Ias¥an4amaoua VE‘OcH-x I. T:- xti-yj‘ b a ved-or ”twig +°“Il "5 OJ’ +106 ori in «mi whose («ng :3 “‘* 4"“ PM “13’- T“”1 F W “’6 ““4 +° sveci‘y “‘6 905.4% 0: a Parln‘ole. Tke (pm-3nd; is lowhé 0.4 HA9, head of We veerr 7-“ ~(0U reac‘n 4kg. earUcle 55 moving x \JnH-s, [n Hue L (horizonh!) Jn‘radn'on ”Mi ‘1 “MAS ;" ‘Lke—j‘Lver-Hml) JCrechon. 2- x and ‘1 are mow‘Ponen’cs o? ves—Jror r. 47 ““1 “U-dcndion , Since “use LhVQhJ-{L'cs are. 3, y Eu“ of Par-MA: Ar .‘5 “\e Jisplacemeni (change .'n 9051430“) AP Q Nol-e 4kg} (1: + if: a (veéors r; amJ AP P an“ using Hug—A +ou'l +o ken-J 40 RH 4-0 Lead TS “fig .' Fluff AF'S +ail 06* T“; )5 LIEQJ- TIM! A sum F; + Ar {5 ‘Hwt vzd-or wLose +0“ “5 'C l‘ x +a{\ .mnA wkosc \nemJ {s 07315 keel ) 4. hr componenlr Ax air 5? gives 44”: Jl‘splncemenJc in “~2— horde-A4“! /j“/ Jh‘cc'kov‘ _ —~--A-;(-—‘ componfwfl- by a? E? aIVEs ‘Hne diSPIOWMEmL in 4"” VEFL'l—Ql _\ ASru’cQon 5. vw= ~ (a Veal-or 44ml- Pomg .‘n «Hue, J magnAQelc lArl ) At Displaceme“; E: [a . ‘ 0L vedor Mn 4 ‘ .1, p M 4 Sam“ Veghr (or a no em PO A .x A Q. No+e 44‘9“], Ar is not {Fee‘l'l‘on as: stplacgmen+ A—F anJ 110.5 ¥ 1 _ {s “we. Parme Movma 9mm P +0 Q. The “+9“ pa+L Jake». consielefeé) 8105+ 'Hnt’. u‘n-‘l-x‘al POSI‘J‘I‘OH P ané 4kg 9‘an PogH-{OA Q. ‘ . Ins +an+0~neou5 +0 7‘ viocflj (1+ P is round [:3 catculcdbxg ’qu a; a 853 do“, t}: “M a — 9‘? 4+Qo 5t E As O QfPrOQLL‘eb P, ved-or K? APPfOQdAE; 44m +an‘jen4 +0 Una PQFL-‘Cleis povun 0-" P. V 1‘5 hangaw} +0 44‘; poxJn‘ch's Pay,“ _: 7- I? x and x, are 41“ (tempo-flanks o§ r ’¢=E‘> V1V‘c+Vyj=ji(xc+yJ)=d_Et+i_-§J\ d J it 50 V : x . v = x a ) \l a): lVl= Spud : W 9: anj‘g velocAY V make; wH—L horizon 412‘ = anglg +omaen+ "l'o TOMS a it pad-k Make; wH-L vK hon‘amhl . 8. The. reasm vecJ-ors are 959A +9 (JesoP-"Le Mo-‘n‘on .‘5 so Houd- Mae. e. 1:; o: “no-Hon have 4kg Sauna $orM In Java ehmevxswns -l-L\o_+ keg/30:14:15,; One. . A . A _ * cl‘menslon . v — i—L has ‘HAC same X‘orm as V: 4x . I? “do“ ”a no-\- vseJ Han 4mm meemsu‘ovqu moh‘on is 325.chng It usm 4mm ezboa4wns- one; Q‘EUQHM Qor MoJricm {h We X Ax'rerin‘on anal (MM-L." 6300.440“ $or mo {on In ~Hne 7 Jfreckovx. Vecjtor nohfiion allows you +0 4e +Le . \ WIN «(BUOAIDM SW +ke x 5mg y J{rec.+.om m one single compach ecbua4-A‘on. 9- Exampk .3. oar. +Le. , x Y wCH ADJ-odds“ “v.5 La. 0. wxhc‘e's posW-‘on be 33v“ lea FLH= (ZUC+ (3-i)j- X: XLH: 24. We. ,( ) (2t) Y: \[LH= 3-{1 34: Dis+onces are 'm Mews, HM; f5 u‘n sec. am! t :0 W) wk“ ‘5 “n9— par‘hclcls [cowl-Con ark £= 35? M7 t=357 Lc] when {5 HM; Par-Hale, oloses+ +0 +Lu. om" m wkd we Lea AJr Mm Mme, 4% M- u.) Wkod‘ is 4kg par’n‘de‘s valocHy \ 7 3m. Mln€mum LLB-{73mm {rem We. pm‘Hr—‘e, 41) ‘Ma is L9) Shh. 4%; ma nH-uJe o? -Hne ve‘ocflni at €125 OMJ veloufl “aka; waq M“ horiz0n+al. :1 1(3) _ a M h): (H)- (a) or “mayo Ho) 4,, if: 2 or v=emls h ('1) VY :- -IM/.> I l 2 ct.) A“): X+y .50 Alt) {5 a. minimum ngy‘ )(z+\/2 wed-0’ ytqufon mgams g org In ? Is Hm ”Ago“ PerpenJN—ukar +0 4kg POSI'4I‘on vector? 4L8 angle +L‘e = (1H3- (31f = 4é‘+e‘—et+9 : 1 . . D: 5*L‘ét +9 =7 D20: lO-EaC; ,) t;3/$5 Sf—éé‘f‘? :5 cu M|mMVl~| 3 m A (?)= “9566)"? :m_ 3‘ 6 J. 5 5 ?‘WF3F=%I\1=2JM 1 b4 4; . L!- : froJUCJ" a: o. .. x|u + y“? ““4 f : xge+Y13 IS 41“.)er as (1-1:: X.XL4-‘I\Yz H' com L2 Sloouun Mag—l- 53$: [allthmQ woken 9 {s 4.“: an 18 Leree-A 3| ““4 t’ II? 9:90, ‘Hnan )a‘__LE| M4 3-: =0. mg, —I .- F.V .2 (:1) (—11) : (20(2) + (3-Q)L_|) =0 445 ‘3 +L =0 4 J ‘ SL‘S :0 a) 4; : 3/ 5 Bacause V‘J‘ l' ) +4“ rAA'QI dl‘él’anu $0M 4k: :l'll in" 1.5 wns‘l'qn‘l' a” “Mfi "will“. (M, “"P‘MEW" or V aria {13 av 44‘ 4' 1 c105“ m. S‘uH-L‘ r S: ‘H‘ .. _ M a a qu ‘CE _ ‘H‘ e Pom e ontn)‘ Tl"a déhmu 9.0M M on In W) us‘ Ln er a. relafi-iue minimum or MaxSMu-u unJer 44.35; 4044440,“. = A v U6} (fl) =) IVl: Speed ; ’Z‘d—L—Tfi = E "4/5 : 2_2 M/é 6: Al‘d'an (13:): Afd'an (.24) : _27o 3-2 Auraae and lns+on+uneoue Acoduoj'ion I- Alu- aae acodevaficn 4. ”la. a : A; : Vl—Ql V1, E¥ AV =T/,_-\‘I‘. I 4&9,“ Q15 \7.+A‘7- You su‘fh‘ov} ‘V “50“”‘5 \‘Y aék'ma yoursglc wheat needs 40 La. 4‘ \ (L449) *0 44M. gr§" ~IerJor in orler +0 oHon‘n Vt. Mae. saccha- 1. Ins-\nn’mmeoos mandated-Ion a. The, ins¥am¥omoous ark-derajtion is leqnu‘ as HR!— “MH‘ 0? “‘94 QVU‘QSO tandem-Hon a5 «Hm Mme .‘vvhnal t. to {1 Lemma vu-y ”M“ - . 45? AV CL = IIM —' = _.- Mun) 5" at 3- Average aua\ua¥.‘on r89.“ *0 a. {I'M-ha has I'd-end , wkHe is We, acceluq’rim a): a. New Pn;v\+ (ins-hm} M +imc). 4. In general, AcceleroJiow amt-l WAN-Hy veohrs :10 “GA-Wham»: accelerd-l‘on "0+ have “no; SAME du'reckon. 5- Exomvhb' An okra-Vs :fl;“':q‘ vdoci’q is 8.0 M15, “-50 N o‘} N- The Crud “gland“! , 305 ‘93”);5 14 “/5, 36°»: 09 N. Who} is H“, amen-13¢ qqderafion? - [Ai\=,/.;-z+qz_z—f—“- = 1H mu“ w W 3.0 ' 2'3 “/51 g;"¢ = Sing =) (b -. Arcsln (fig 9:“9) s Arcsin £2 5;“ 25°) : 23° W| [AFN “H 7.0 (NM-e. “55H 7.0 ml») M36“ so“ AV «ml Km"; Make “41 N _ w ’ So 0“" 3 2'3 m“Is"J 53°W a? N- am angle a; 35:- 23°= 53° 3‘3 %Mzonen*5 og- ALLLlerahon ’ c. H -‘s «Shh nonunion-i 40 work wC-Hn 44w coMpongnh oS‘ acceleraA-Con. m=fl=fl Ma ay=flti£L3L 6*, 4t?- dt d%‘ 2- th-or °°°\’A‘\':0'\$ -. a" g E t 4. all A : if 6+- £1 ,. t it J ult‘ At‘ J 3. W‘ntn a Parke“! Moves on o. gut-v9.4 PaA-L” H .‘s somekmw convenienl» 4.0 1,..qu (Perpuéu‘nuhxr *0 {'Lw, Pad-Lt) and +an3¢n¥fql (rqrallel We ma‘eroA'fon {uh normal 40 MA: 90*“) meanen-k. Nah: “no.“ a“ is. +Qngen" 3:: 44.2 chW 0M“ ““5 I’m-"*5 i" ““2 same Aireahon a; velogfly 7. AS 44.; Par-kale. movu, H"; JirzGVOV‘S 0: We tamponen-Lfi a" and a; clam-nag (when 46 omJ ‘l oomvonevd's are useJ, HAe diredu‘on a? Mag wmpnnenk is 36x24)- TL; “Mfonefllr a." :5 “a. Mmponen+ a: a 444a“ GLOW?“ 44'“ Magnfluie or V. The, cemponm+ «1.. a; 4L“ ““9““; o? a- “a“ gknn%e."> V '5 Jirac¥f°n_ 4. Nken 3 {a :de +0 3) H5 (Size! .‘5 *0 (Jung: +ke Ma niluJe, 0?? hair no¥ L4 He. ‘Airachen- when a is perpznéiculou' *0 ‘3 , {Ls eS‘Qed- is +9 “Mr-3e “he “mayo" 0‘; V bx)" Ina” i’rs nuanHuAg. S. 19 a ¢:r’~{.~,\e #r‘wds on a cur-veal Pocl-L. o.-\' wns‘fln‘l' speeé, +L\G acceleral-{on is no+ zero. v :5 wonaivxa because .45 Jkedion is 4mm {na- Since “n: Spti-J is no" 5‘“°‘“3;"fl; 44", acceleraxbn :5 always Pargemliou‘au- 4o +l-n. vdocfly, when 0. Partial: MW“. 04 cons¥am¥ sPaeJ in a circular pod-k, 44w acceleraA-u‘on Is always Al‘rEcHJ l’owm‘J 44M. can-hr o§ We circle. Velom‘fi {a parallel {-9 We oft-519, L+an32n+)15° a Qupmdécuhr Wang-hon .‘5 Jwea’re3 Rowan-d Hm cirolg's Nader. 7., _ 4v ‘7. Ta VI l». IXQMP‘C- A parkidc‘s @oorJina‘Veé are X: 2% E y: 1 m— L4.9§1)£1 Fmé Haw. Posflion I ve‘ocH-g anal accdy-akon ck k: .505 x . {14; J “-5) \ _ 1 = = fl X =l : . as (Y) 2-4.9: (1443”,); (.78) m, y 78 a. x’ 3 z _ 2 _ z "‘ (‘1‘) (-3.3%) ' ((-9.s)(.:)] ' (-4-9) “7 V“ : 2"” V1: “'9 "‘" *k “’ ‘Hn r I I‘ 1 No“ ° 5 595%; 9V 'H'“ pa. ‘0‘: 5 " Va + V: = 4(2):“. (‘1.9)‘ = 5.3M/s anJ “at any. 9 44¢ Pad-k makes wH-k HA; Inoru‘eon‘n‘ {-5 9=Arc+am(!1) .‘ x" O :Arc‘cm(-‘: )= _v280 0.: (VII): (_9'9) =7 (in-=0 J “Y: -3.3 nan/5‘ The. occehmlvmn r; Joann-Jul wHL MGanH'UJE. 9-9 n/52 ‘1— EKQMP‘Q. A Porhde‘s exuded-alien .‘s ;= (1L): + (2 4&3) "- L". " ‘5‘ ”- alf '5‘ 5 t. The _‘_ H _ _ - ,wfeovyn14"“‘- PM‘M—‘e 1‘“ ”5* 0“ H“ “‘3'" 4* ‘7‘0' Fm; Hue. valor—$3 anJ PisH-‘on wed-or; .5 ‘4 L5 $0an L3 in-‘egrakha -u\e comeonen‘rs or 5‘; 1 ax=2£ -> v,=t‘+r_ ,vLo)=o-> Va: 1 l .x =- .5- 4 _ 4 A I‘ n1: 1- 4t! ’7 V‘I = 2i - +‘fiC, Vy(o)= 0 1:) VY u. 2t‘t4 > lgt'LtV‘u's+n‘n(:£/s£ ) f' r is 9‘»an Ba in-kegI-whng Hue MMfOnEvH'L o: t}: ~.-.. 5“. 0m .5 l \l : ‘9 -. -L ‘5 i J 1 'L x at-rcl XL°)=0‘7 X‘si ,3 Fl: $t33+(t2_lts)a v=2t-t‘-) =t”—‘+.’c ¥(°)=°é7 t‘~‘e’ ‘4 ‘ a y y E + a _ y‘- 3 wk": r -'s in m and-£13.}. l- Examp‘c “L (A bauoon Cs +Mrouan Cram Aim, orig:r\ ad; i=0, Th; Gu¢leral-:on a; “a: Lquov‘ .5 33: 1292+ Q— (Adj, when: 6‘. is in a ,{1-‘5 "“ SEC- U720)— ¢(°)= 13+,2J‘ Ln N‘nw‘ F5 Hue. MMCMum Mel‘fl‘rfi a? Hap. haul-10"? m How 5.2.: Aces we Lawson lat-«<1 9°“ #6 my"? La) fly! *4“: a) V1: “‘3'tz+c 1 Vr(°)~‘-l1 ') V1:-3tz+l2 y: -t3+12t+c, y<°)=o a) y: 43H“ Y.“ =7 V,=o =7 ~3+l+lz=o '- 23+ 11 , 1:: 2 -> ya“: ya): -(z)‘+|z(zJ.-. up...H Lb) 11‘: titz =3 v‘: 4i3+¢ , Vilolzl I) V; 3 4€3*l E %= £4+£+¢ ) xlo) =0=> x: £4+t P ‘9‘“ = HIZ- t‘)= 0 =7 l2—tzr-O =7 t1=|1 , so x: rm 2 (mum = ISO M wken Mae 3-4 Prosec'kh Mal-RM bal|oon 1. V‘ajgdiie— a \ooAy “Md is stun cm .‘Mhal velou'kl and 44‘“ {5 add upon onl b3 3rav§+ou\'iom\ accelerofiion anal m‘r residomce- EXWMP‘EJ a. lav-x4494} ba$¢ba\\. 2. Trajtc¥oq~ pad-la :oHowcA LP a. grod'edn'le 3- Ne win emA +kese Sums .‘n oor analysis = air nagging) drums: in audamhon Aug 40 arawhka NHL heifllfi I egged o: ear-HA3 ro+a4fon lqus Y 4- CoorAKnoA'eS ‘ ‘l[ ax=D a, 3 - x 8 The verJ-icd who“ has ¢Dn5+M+ Amlermmcma “we Lot-'zoM-al nun-Hm has (Loud-0M vaccflr . 5. vfojcd-Wz who-hon :5 enables-\- +o analyze, one wmpmen“ 03 a. 'lime. The x and y componenk as make“ can he mqu1c$ as E? 44.13 ware inhpmdent. 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(7.9)(IBO)1 ‘ R ° t2¢o§30)(|50an30—23) = 42 m/s m =v,S:n6£—-§gia=) v,s:.\e+. = y+ nae: 7+{8‘I' =Va6058£ v, Onset: YX x x Tame : y + 2 (xTage— —y 10” Ta» 30- 16) 9.8 = 2.94: |3- 2‘3“?“ A Sou-er bu.“ f5 kx‘ckeJ 25M. H's max-mum 1‘ch I3 6-0 M- ;a) win“; .'s 4-H. :ni‘n‘al veJooHy o: +ke \aaH? “A How 10mg {5 #9. ‘90.“ M Mae air 2 LO.) ‘1: y°+ v. 5:091— fiat-z: S-HB'L ‘ 'Lj‘kz x sx +v.Coset~.= V.Cn.59+. V : ‘55-‘49 <3'L v1 : v C059 maximum ku":tof\"‘QJ A‘s-hxnce': roman R “=0 :3 Maximum ku‘k‘t =3 0 Va s- 9‘ .£ 3) i Va Sine 3 = u‘ 3 MW MM: i“: 291"“: 2Va Sme 8 3 Q: VoCosS£.q= ZVOzSMS C059 - Vet Su’nZB K — x = ' v a MMZM M ““3“" => V.,‘=V°; -23AJ H occurs wkeu 'v-_o. V95: 9 - = n — _ ‘ L‘ n ) 23H 0 3 H- m ('H-ub PESUHV can alga LE Sauna H °—z— Tune V ’ V‘*V=5""9t- 1 t‘) .._: 3 : * 2;, 4H 2.5 ‘2 1v: $1.9 C050 4' Tom9= R x a H : V02 Sinle -> v9: 123“ by} T n 9: 4—“. s c = 4“ 23 5MB :1 7 5A9 K M: a ‘/ Q‘+ mm A“ v = [25“ JR"+IbH" - (magma—T (25)‘+vsm.o) x - 4-H K = l m 4“,.“ b /5 Lb) km: 2Vo5h~9 = 2.4.111 Sing Sine = ”is“ a 2Jc2)c9.sm.0) 5225 a 3 ‘3 9.8 u. Examph (7 A boy “area’s l bu“ gram a 5“? a.+ 0- dtvar'klre «nah 09 923500039“, 4-H, tun-F2 4-! M {AH-Ea»! vflocf‘lj 0? l5 «[5. H- hands ‘60 M cram u“. base n? “we ch‘CV. on a «AA (0) How \m‘flk is +sz ch“ 7 U‘) Wkad' :5 *ke Mme. o; SIL'f‘k-‘r? u.) who.% {5 4&2. velocflg Canaan-'4»qu omJ difECJ'fon) 0? Mac ball wkcn H shakes +La Swami? \A) y: Yo + v.5{ne { - iflJcL 2 .7 = +v 5.1%; -1 L) X:V.Cos9£ Y Y° ° A muse) 29 (meow y : 10+ xTame - #3 x2 2 V,‘Co>‘9 7:0 wktn M Ln.“ lands. 2 1 O: . T - J' ~X = o = i X " Y +X ““9 1 vozcoaza 7 Y 2 9‘1. Costa XTQV‘B = L9.s)uao)" _ - x ~ 103 T : - u.) -v c Be. a) X - .50 ”H'M‘Mossé)‘ “3° 600" x— ., as *‘vocose —\ = |2¢ (I5) Cos 36 Lb) Vi: Va C059 V5: V0 sing —3£ = V0 S‘Me— L V0 €089 v: (vfsvv‘ I (v.6ose)‘+ (wag—L =- V0959 [(AE) C033512+ I .5 Sin35~ m 1‘ 3 no «ls v v S 9 x (15) Co: 36 _ ._Y. - n l - k _ " ‘9‘ “d“ ( w ‘ AWN \vcw ) 2 Arm“ '55-‘n36 — m 35" V. C059 (IS) 605 35 6- Lumen A baselmn i5 ‘Hnt'ovon wi-H‘ (1 599,“! of 35 m/s . The '0 - 4 «nah. o: 20 uan 4k: koruiond‘od, ‘0.) HOW $1” 4095 +‘n9. bah \Omd gram :4; 0,) How to“ is We ha.“ in “M; m'r? Le.) How h: k Aces Mae ball ruse, ? . ‘ A . ' 7 “n wkai- i: + e banks VMom-H {Ma mhxie, am; AIl‘uhon) w‘nen H’ lam-ls . K“) From Hue sdohons +0 Example I3 I5 (.05 36 velocHy .‘niL‘aAlY makes an orig [Anal 9 osx‘ 'Hcm _’ 2:“: 3:..ecose = v: S-‘n 29 g L36)‘ Sufi? _ 9 9‘ T - 5 M Us) From “me soloch +0 Example ‘5 Lma = 2v.s:.\9 = mumsm 2° _*= 2.1; g 9.3 u.) From 4‘“; Sal‘s-Ho? 4o EXAMP‘: l3 H: v,‘ 5.39 = L36)’s;..‘26° 23 L2) (9-8) ‘4) pm... 4L“ 3 "mar; 05? «We +rajec¥ony +L¢ 392:4 anA A.‘red“on o¥ Hue Lam luau/c Hm same Ma nHuJe; when +he ball 'th5 0.5 H" ““3 wLen A» was +krowé. hi! a 59924 = 35 Mb 9 = —25° = 5-4" 3.5 Cinder Mokon “a \- Unicorm chauhlr Mekon'. 2. Q? fochirJe moves in q c‘rcu‘ar pad-1n a+ wns+qn+ speed. 4/ 5—! = 0—5 (Simi‘m’ 4riqn3les) XV V R V L V -7 13l=“—-"= 3- *{5 Q At R 2% Z Wu autlemkm is adulaup perpendlodar +° 'u" V‘l°"“’1' TIM”) alwaqs JireerJ +oward We nefl'er ,“xe accelemh'm .‘5 cc “we birds [The acceleraln'o.‘ 40 We GHQ—6+5 P‘fik- ) Tke moan\+uJe o? Una, acceleran‘on '3 L‘ R . 3- The, acceJerakon is come; is ACred-ed 40.41“} Hm (mark? a: Hag {.5 perpendu‘colar ccnhipda‘ accelerahon Lemme 3 cirde- 4A Perioi ’L’: L‘mz gar one revolu‘fi‘on- v: dCshxnce __. one circumgerenae. = lTYR +ime, one, Verna .) a : ."f: M‘ez/r‘ = 47:19 T: K R AVMLer a: tumult-$0.45 Per sacoml. 5' Freatuencxl Q = g-.— 9*W‘Ple : W ‘1 S¥me makes 5 ruoluhons {n one second (9: Sgt) Hm” em women «Lakes gsec- (”k ? 3%) v: feuolu‘hov/B x A.‘s+an¢e sea 6- 1S1 Hue span! is = $ (21m) =v a: if: 4192‘?‘ m z “"22 $1 rev ‘2 R “0* cons‘un“ “men “new is a. hngan-‘(al acceler‘OA’VOn wmponen+ .‘n “AACL‘on 4-0 We norm/ml accelerahon OOMPOnQI/Vt.‘ a = AVA! u Th when HM; $99.98 (5 wn$+an¥ Hag-e...
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