Study notes exam 1-d

Study notes exam 1-d - “p~|{yxwvmEUs }o z u ut q ppo ngmlg...

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Unformatted text preview: “p~|{yxwvmEUs }o z u ut q ppo ngmlg ig f d˜ re‚…R1…kjh€edS™— •–“g‘iqr”“’‰ ˆ‡†…„1iir‚R8€xwvu tPp ‘ V pgXg ƒ ppttp V Vp y gtX PptT sPpgg f d Q b YX VT I QP 1iW¥qrqih§eca`WSWUSR2I 33 )C3  5 HGF£ (A 0  '  EA 5 D C 6 B0 @9 8" 75 4  A  ' 6 3 21)¥% $©"   ©§¥£ ¢ ¡ ' 0( ' & # !    ¨  ¨ ¦¤ ’ (  8 E%  5 (% ˆ% Œ4 e ˆ ‡ k 0 0 ‡2 ˆ2 ‡ †… … ƒ ‚ y ~ }| {x yxw v u r qo n  2 02 " (4 B4 k% — 20 ‘@6RŽ'Ab6P˜@b‹!Š‰3px@t„Cttoyv}€¢vvtƒƒtz¦bd‘bts”rvqtpR!F!m A'AD¦!l˜jA!(     ’ˆ 74 7 ( g 2%2 e   ( (  2% ™ 2% 4 0 —422 E • $% ( 0 ‰ ’4 ‰ ˆ ‡ 2  8 E%2 †  ‚€y w siqi ! Id92'!A9ihR3r3bfA'! Ap˜'d˜r)A'@˜'A!!1–C”5@‘“A‘x)x@3VRA…„ƒ¨XS xvutrph g ef e ca Y W U S 4 E 0"  2 B 0 2  5 E2 5 ( % 4 02" E42 7  2 B 0  E 4 B 5 ( 7  5 4 % 2 0 (  "    ¨1@db`XVT!!1@AR3Q¢!P( !'I1)@3¦!!'9(H!G6!F@D0CA@98! 6'¢ 31)'&%$ #!  ¥ ©§¥£ ¡ ¨¦¤¢  ›˜˜ žœš™˜ Q ” ‘T g 7q“P` X V 6p ‘ p ’ ˆg“i”T D ‚@g V c¡aVhwT €at€wr—‚qjtp ‘’ g i”T D ‘t 3'–p ©aVit ‡Sqg qw2• ‘ ‘t p 0 ‘ C ‘ ’ s ‘ PX6 p 0g — ‘t ‘ ” p 6 ‘ g X 0 pg T s ‘” „3'p g s ‘ ’ “ c3sp g tc‘ ‹c h c „3'p g f c b lYW s ‘‚ r s ’ s ‘‚ X X g X xi = -30 m xi xf = 120 m xf O STOP x Ž• j { n {  € ™ f v ” f f • ’ ~ ‡ … j f” { ~• ” ’ '3‹3Vwi’u9Š”¡Œ•‹Š”‰'}ˆ†©hsg#wB• s}™ n m ƒ ‚ ” {“ • ” { n e  f €f • j z j f ” ™ e ” { ~ • ” ’ ™ ” { z jf • j e  v j ’ j f „ƒ7P• Vqe 19¡VFh•y@'u©hsgA¡• PwB…• s}|9wuy@'¡Vxwut©hsg” ™ ” re • l’ ¡qRp otl¡ie@h•gt3d˜s—R–3’ • §37‘‰ n e“ n m k j f f ” e ™ ’ • ’ ”•“ ” “ ’  } ) ˆ's† ygd yS§…s ‡† † & i ˜ „ r ‚ EE ƒS iiE h ` xX € f x X c b x X ayW S‘ V C X s ` V X V T‘ 6 p ‘ ` t X T”37WWaˆg 7iP 2WS0 r p EE sqS iiE h S‘ ` P T TqWT r6 v wg U p ` f t‚ˆg • “gˆg WSf FwT g 7p ’ at2g Rp rp tvXY D atI ~q ‘ VX u P 6 X ‘ V s 6 ‘ } QgV sp6 ‘ R…rp r13vXY D at` g ©ed¡aYW f X c b X ` X U t pg X Vrˆ‡SV } Y ‘ ‘ ` V Y X V 8 t Vpp Qgp 4 p6 VpP ‘ ` p 0g 4 V C WvXˆ“g ‘V WX wSeFˆ“g‘ r1BR1{P1©rirp IHc‚@• Grp “’‘ Fat‘ g E ro Q WaTˆ“gi”T D V ‘ ‘t ( & u p 0 t ˆ“g‘ V ‘¥”C¡wXSB6Ap‚@g WX Rp‚Ve9‚` at‘ g 67p 5©3T wXB3T rz gki g © d˜ 'l Et ‚1y } ) p V 0 0 t ` 8p 4 V 2 m } zg ( & % ”m jki g © d˜ ' ul §}  ¥¨ "  ¡#!   ¨     ¨  ¥¨ ¦ ©§¥ ¤ $ ¢ £¡¡ € †x “ …x “ ƒx g x U ` p‘ Br R“aY D s Ga€“2hStyT rˆjqB‚W…FV Rqg ‘ t‘ g‘ g f 4 E T 4 g C p g P f T • ‘ V p S ‘ ig ˆP Q wV t ksˆiwhwT g 7p )‚@yh ˆ…r‚”T D ”16 Wˆg 7p 2wviRqxwX V g T ‘ Q T P P X P 6 ’ p 0 g t g V p V s T P T 6 ’ V X‘ t p g P t 2 s ft p 0g t PT 6 X tp ‘ Q E T 4g Cpg P fT • tXpPp 0 ˆ“g‘ tT i¥‚@WX Wˆg 'p ’ Rq“gqP GyT rˆh"q‚”…WRir‚‰Q EE r ’ S iiE h ˆ † ‰Y g ‡ “ Y d „ “ Y X „‚g  … ƒ  x U P g V p V „sqWT 2 …r‚”T D ”raGwT g 7p cqg ˆP lWr—p r— B©i€t B s T 6 V‘ P 6 ’ X p ‘ Q V X 6 Q 0 6 f t r Q Waˆg X wGwT g 7p G“f ‚@g xf w€rp ` V T‘ g T V P 6 ’ g‘ V p 0 p t g T V t T E yT Trˆh"qg‚”T •Ug S@g qw2• Y1rqg SaqWT rFwa”T D WT 2 x8Y a2Q 4g Cp P f X 0 p g T h Q t p X V‘ ` P T 6 P XY P p t f Y‘ p Q g 0 Q ‘ Q Vp ‘ VT6 ‘ pEX Tg Pp `PT V ‘ gT B‡XS‰a0@“g2g Rqg atit”1…g ”)7s ˆBr‚qW ‘V ”aTˆg X wV f UbX p‚q"3T WRˆg tV Urˆg‡SaVqPWT TrdWXvirqiP X V WT ‹qWˆg 7p ’ g f ‚@g 0g 2 ` X p ‘ t p X ‘ ` 6 V ‘t pg P 2 tPT 6 ‘ V p 0 P 2 YX S S R V ‘ g v X 0 0 p t f ‘ Q t t Y 6 ‘ 0 WT ˜r x—–¨wT5$h ”aTˆg X wTV (g Stup‚@g7xvaYaY2tp Q iWvX1|t qg V E @ Q V ‘ 6p ‘ Sq Y hY q U ”aTˆg 'iP ` wrP vX”T h ¤P Q iU ”aTˆg 'iP ` iP waX”T Yp V ‘ 6 p ‘ S P Y V 6p ‘ Se V ‘tpgP ” ‘T g 7q“P` g`WaXiRqxwX xf U Q `WT Yg P h t @ € @ s( u @ P ¤U u euu V ‘ 6p ‘ S • V ‘tpg WaTˆg 7iP ` d¥WvXirqiP X xb U Q cWT Yd P V @ a V euu @ a @ Q `WT xX U ” ‘T g 7q“P` S WwvXiRqxwX V 5u YX P V 6p ‘ C V ‘tpgP Q –“gˆg WSju Wˆg 7p ’ •‘ VXf PT 6 X t”T ˆg 7qWT ¡aV8wS”aTˆg 'iP ` ‚@U‚• p ’ ”16 “g‘ wg WaTˆg 7iP ` 2 T V ‘ X sP 2 ‘ Y X V ‘ 6 p ‘ p 0g t VT v V ‘ 6 p ‘ X WUsp œ—¦UT5!• g f t„‚ˆ“gV ž7s X WS0 {RWdg Qvmu z I B ` V X r S SRh ‘ V 2 T p ` f ‘ C X t X n x m ( P Q qt GS71‚qg T p ”i€W— X ‚q„¡”T WX p 4 r ‘ C X — P p 0 sTt PT p 0g C V Y •X YX ‘ p Q gX0 QTVE t X YX Q 6 ‘ `p`ppV gT Y R€TQW§aYaY2Q B1‡Sqg sjFh• GIQw„p —p ©aVit R‚rr‚wV • aYWX S f 6 X t‘ V ‘ t V ‘ p V ‘ V T‘ g T V P T 6 ’ C V‘ t f X 0 g p g T V †ˆg tvac”T iRp s ` ‚”T V c”aˆg X wHWˆg 7p ¡aivg S@Bqweh X Y X 6 X 2 ` p t V xX P T 6 p ’ X t ` p g V p t p p V p X YW P vWrt GtT wX qg a‘ yW Wˆg '”„wX rq…rxRiP D qP R1p 4 p RS0 a`Wˆt g Rp rp tvXY D at` BsBS iiE h Yp D WSDu aV‘ • aYWSˆg 6 B ’X Y fT 0 V s 6 ‘ —rp EE sXC YXf @ H ˜ @ A U t P T 6 p ’ g‘ V 7qWˆg '”G“2‰ } 9 „ ˜˜ 1œ›š™˜ 8 3 43 2 0 ' %#        ©§ ¥ £ ¡ ¤5765!1)(&$"!¨¨¦¤¢ t c” s ‘” „3'p Q g V”T ˆg 7iP ` ‡p ‘’ g i”T D ‚@F ‘V ‡As ‘ ’ ‘ 6p ‘ C ‘t p 0g tb t ‘ c c” t f 5db 3 3 c 3 4W r s ’ l„‘ Fc h c c3sp s ‘ ‚ g f ec b X g X W X g 2 g Ž ` f  € { U { s “ { U ’ W“ ’ { ~• f • ’ ~ ‡ 3ah•}†he3wYus’ 3}” X37 wBŠ”‰'}ˆ… X W }V‹• { U e n e ” v j e  {” S ” {R • ƒwr7VATVB¨’ h•f u9is£1PqHGFEŠ{u|utCAy9 { n z ”” ’ Q I ‚ 999 D € ™ n ’ B @ j } o ‡†† r8ˆ's† ygd yS§…s & i ˜ „ Q ‘ ”p s ˆg tiqr”’ rˆiw YT D g 7p ©3T ‚@tT ”aTˆ“gi”T D ‚qtT 0 D ˆ”Fc”™t g aVWT D wSe8 ftPp `pgg 6 5 4 p 0g 2 V ‘ ‘t p 0g 2 XPC X VT ‘ YX V ` V Y ‘ ‘ ‘ p 0 C ‘ ‘ p Y 0 ‘XP p 0g 2 wX WvXˆ“gV ‚@g ¡V aV”T 5 ‚aV‘ Gg uICWˆˆg t ‚@8tT p D T it ‚@„ˆ~wSj7Gat‘ b 3 Y p 0g Tg YX f up T g f 3 Wwx1ˆg aVcp asˆg ‚@F¡aVq‚` g 7p ©3T WX tT • g r6 aTrp ©”žX 1p RX ‚1y ro YX’Pp ‘ ‘ p 0g C ‘P f 6 5 4 V 2 ‘ Y ’ p C P ’ p 0 } r 7 EE †8S iiE h € f 6c b 3 3 f xX c b xX g 3 4W xX yW g x2 U f 5db 3 3 c X f ec b X 3 4W X W g V ‘ gTV PT 6p’ P ”T ˆg X wGWˆg '”FaV‘ wT g 2 U Rii‚176 Gg rp Rp taY D t ‚@FBœ‰Q ¡V ˆ‚~wwi1q…V p s ˆ‚@g …4 ` p P P f 6 T V s 6 X ‘ ` p 0 g 0 6‘ 0 C ‘ P f ` Y X ’ P p g ‘ ‘ g p 0 • ` ‘ ` V s 6 ‘ ` p 0g t `p V 8p ` ‘ 0 u g P g & ˜n P p 0 Rp‚` ‘‚’ vg Rp rp tvXY D at2‚@HWX r‚eV‚vt j— 2 — 1vm…( dx {ce'w…g ˜ ‚1y } ) }0 u( ( g&˜n e1vm…wyxd g )e'w…g P $ } r s ‘ ” p g r s ’ c r s ‘ ‚ p g c b xX € Y X l„3'h aY X tc‘ ‹c h AY X t„3sih uf x X u¡x X g W U ”aˆg X wBWˆg 7p c¡a‘ V T‘ g T V P T 6 ’ C V St f rp StqP D ‚q¥rp “Wqp RSla”1p Q BsBS iiE P Yp D WDu V E @ g s Y 4 T p 0 g ` ’Y T t ’ X 0 `Y f T 6 — r p E E h s X C Q Vp V sT6 PT 6p’ V C p 0g 2 p ` f Rg R‚”T D ”1Wˆg '”Frp “’‘ #‚@™3T ‚ˆg S‘ C X s $ P 6 ’ p 0 g ‘ g V T 6 Y V TV 3¥t wT g 7p ©‚@V WX …WrG• ”T • ‚@g wg qwaWrˆt Y WciwX p 0 v t P XY X 6 Y X p P `VX … — EE Q p t P f T t‘ 0 g VpV sT † ‡ w— „ ˆ ƒ  Br ’ S iiE h Q u u V E Wxq‚”r6 a@F ‘V t g r‚”T D Wr6 PT 6 2 V ‘tP tP p 0 C ‘t f p YX 0 p ‘X C p6 Wˆg 'p ’ tT ”T iˆ1p ’ g ˆS8 ‚@g ¡aVi7{4 aYWSt BQ — aVW…žX 1©V # † ˜˜ Šœ›š™˜ % "  # #  © § ¥ ' % ¡ ¦¥ !$ 3 ¡ $&¨¦ ¤£( ¢ Q aYw7it YX s “•Y WX7asitrq“gVe8raV‘2rp ”1'p{4 34W WwxP1q…V ©p ‘s g©‚@g WX –“g1†T Rp ’ ”3ˆ1p RX Y ‘ p‘ t sT6 YX’ pg ‘ p 0 t • ‘6 Y pCXP ’ u l xg z z˜ml p0 p ‚0@g 2tT g ‘¥as Y‘ ‚qgWX@r‚Ve9‚`©at‘)£x 2 — 0 m …( xyd g P 8I …8S˜ m SR18 uz ‚1y } ) p0 t `p 8p — }0 u e1vm…( dx g ( 8I x 8SRm S˜ m 8z §} l gz˜ z l † Q V”aT‘ˆg 'pi“P‘`C p “’ˆ“gi”T D ‚qg aV‘ 6 ‘ ‘t p 0 t„‚ t p ct ’ s p g c‚ c s s ’ g t As ” € ‘ b f R3 c b 3 X f yc b X  g 2 g 1s 2s 3s t 1m 2m i 3m f slope of connecting line is average velocity x … VR3heutd9V{ ’ Bwq!3e ah•}†he3wU v {•• € ™ `“ e•   “ • { ~ • p ` f  € { { s “ { U ’ { ~ {• € z € ’  Q ¨ € { ¦ ~ ™ “ { ~ n e“ us’ ž}Awq• sŠ’u3hu'T©Šežt§ud’ ¡s wq• ¡q†¥ } §ˆss† ygd yS§…s q ‡†† & i ˜ „ 0n xm ( g£ ˜n Q P{RWdr¤wRm X rp aYwR#t RW)X Ug 'p ¡tT ‚qUg S@Uw YT D g S@g ”T q‡X D ‚@g tp S3aXˆP w’ ` YX6 ‘ tpE g 6 5 4 p 0g X 0g g X 0 V 0g p 0 — Y 4 ‘ X } Pp 0gT sTt 2T V ‘ 6 V 2 X tX Y 4 ‘ X X 2 p YX’ p 0g C gg Vp 1‚@w€p Wqrtc”aTˆg ©ef#vW€p S3aXˆP w’ rtT ‚afWwG‚@¡ ‘V iw YT D r‚0 ¢ ~q ›˜˜ ¡œš™˜ 8 3 43 2 0 ' %#        ©§ ¥ £ ¡ ¤5765!1)(&$"!¨¨¦¤¢ ∆t t slope of this line is average velocity ∆x P x Q ‘g X 0 Wp asˆGg S@g g X –“g1†T R”€WR‚WX g WX g aVc‚@„p –ˆg R‚e9‚t „p x‚r6 p asˆg • ‘6 Yp ’ t fTp V V t ‘ p 0g 4 T `p V 8p ` ‘ ’P f ‘ S V T‘ g‘ t †Waˆ“i”T D ‚@g ”‚a Y‘ …r”¡WX g ‚q~tp D aiU‚@Wƒ“awRœ0 D ˆb p 0 V T p V g V p C V p 0 g 2 T TY t p 0 g — •YY X 6‘ X P Q TPp C ‘ 06 T D q1re ¡V BtX qP ©D X P1ˆxWt WCrqxWH1”t— 4W — Wwx1ˆg aV‘ p s ˆg ‚@)Wcrqg Safww1p pgPT 0 ` VX PpgPT 0t gp C 3 YX’Pp ‘ p 0g tX `p X YX’ p 4 Tg {ˆ ‘t 3 3YW aTˆg ˆP ‚@g S@UWRp s ¦¥as¤Y‘£ ¢ ”T ˆg X w¥‚1y ‘ X p 0g X 0g t VX § V ‘ gT V p 0 W  X @ s( @ H Q rp ’ Yp j"‚V ‚@G‡€rœ6i‚• 0 D tGw…R{X Y g Cp p 0g gX t ‘t 2T PT ’X  f”…Gp”’“‘ ˜ˆg iP1‚0“g‘ p ©fjqqg aV‘ g f 5 E tiq‚”1§at@g V "af1–6wR6 T• C T p p 6 ` TP t —ptP fT6 ‘ 0 ‘ t Y f YX C ‘t ¡V qf p 4twT€YaY 2QGp Ag‡XS0qqw2‘Q X Wˆg 7p U3p “ˆg w’ qr‚` g V ‘ Q g p g T • P T 6 ’ 2 T ’‘ X ‘ P p p as‘ˆg ‚0@g t ‘F`wX f fr6œWr6 s”qyP2 at‘ WaTˆg X wV 3 © x X © ‚@g ir‚‰Q p V t Y YX T V ‘ gT  p 0 pPp 0 © 3 § ¥£ 4W ¨¦¤¢ asa‘Y ` x 2 xX yW ˆ 3 © xX r EE ƒ” S iiE h ` U s P 2 V T‘ „qWT l”aˆg X u Sf 'p V E ˜ @ A "  # #  © § ¥ ' % ¡ ¦¥ !$ 3 ¡ $&¨¦ ¤£( ¢ ›˜˜ ¡œš™˜ Q rrp D t `p t”TR‚w†g WX g aV7WRp {aYaY2Q v ……H'l t qWGF‚q¥W¥• g r6 aTrp v”r‚WX g f p VX V t ‘ VX s ‘ t g g & `PT Q p 0g ` VX ‘ Y ’ t fTp V u g aVFWX p raYY 2Q v 0 m …( yxd g P t qWB‚@…— qwGweT2 …V ”T D at@g ”qP ¤ ~q t ‘ V s ‘ `PT Q p 0g `PX QP g ‘ ‘ 0 sT } S V †WX Q ‘ ”p ’ ˆg S}…Vp‚V {4 1p ’ ‚V Wrr1p D H— ” ‘T g eV‚„t @g ”qy2 1©r2£Q –“1†T R”’ X C p P p V X 6 ` p t V ‘ V 8 p ` ‘ 0 s T P p 6 V p ¢ • g‘ 6 Y p t T V V t ‘ p 0g 2 p ` f ‘ CX pg YTt 4 p 0 tX `p V 8p ` ‘ — ‘ f”Rp‚wX†g WX g aVF‚@GtT ‚ˆg V 37s qhafWqSžX ‚@g W@R‚e9‚catCƒ• g ˆg P vXWr©Bt 7B–6‰usg 7p ¡tT W§tT ……Hsl 8A…8SRm S˜ m 8ezu ‚1y ro YX6t X ‘ 0 ‘ 0 Q — 6 5 4 VX 2 t g g & l I x g z ˜ z l p 0 } S V X f †WSju ∆t → 0 ↑ lim t slope of dashed line is instantaneous velocity P x ∆t t slope of this line is average velocity ∆x P x ›˜˜ ¡œš™˜ 8 3 43 2 0 ' %#        ©§ ¥ £ ¡ ¤5765!1)(&$"!¨¨¦¤¢ r 1q1p Pj2hf D V ‚@8tBˆ“”œ€g Wr6 IV Iit Q t P 4 s f V g ‘ p 0 g 2 T t g‘ C‘ ` V X 8‘ C‘ p‚@g 0@“g‘2Q g…Vrqg tait”16 t ‘"g 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xcžsp g  d — s ‘ ” — % t As ƒ‘ € ‚ g  ¢ rp “”C iwX p Q £c  2 ˆ3@r‚ˆ‚ˆ©a‘ ‚a”¡RF‚@g b ‘ V ’‘ p P U H T ` p V P f g t p V‘ C V p p 0 ¢ Vp 0 gpE6 TP p 0g 2T • ‘6 Y ’ p 0 p Y f YX6 Tg `pp V ‘ p Q— t r‚‰Q 1”(†qG‚@{3©–“g1†T Rp G‚@g qg vX1–6Wr˜ˆcrr‚haYaY2Q Bt'g ˆ“P‘ ¤ U 3p D Step 1 a1 = 2.00 m/s2 Engines shut off = y1 Step 2 a2 = -g = -9.80 m/s2 ymax y Ž• ~ f { '©hsžw~ y1 = 150 m t1 = ?, v1 = ? pg q…ƒ Rocket while engines are on vo = 50.0 m/s yo = 0 to = 0 a1 = 2.00 m/s2 * y ¨ g uœCr‚0 G¥s ‚@g t 2g S0 0 ‘ p C X p 0 ‘ X ˜ ¢ A @ ¦ Ž“f { ~ jf • { R e { ~ šyƒ’ wB• y…gBV q“ wB• Š”f s¡Še€ ©e s j ¨ n z u|n f B #n Rh•„3w7q|gBR †qawB9{ uv ¡e X• hpf ‰ž• 'xs¡Še€ ’ ” f ~  ’ {“ • {  e“ { ~ • ” e G € “ { p ’ s j I P D ¨ ©e ¦ "  # #  © § ¥ ' % ¡ ¦¥ !$ 3 ¡ $&¨¦ ¤£( ¢  ›˜˜ žœ™š˜ `pP ftX s t § tp 06Xp pE TP p 0g ‘g p 0 Ri‚iWRp BwX ©¨¥ d r‚BtRiP g ”6 q‚@€p asˆU‚@g ‘t % 3 wX  d r‚BtRiP ` V tp 06Xp g ”6 qU‚@¥R‚‰1p s ˆ‚@g ‘t  3 ƒp s ˆSWaXˆ“gaV‘ ‚”T WGAB–6‰d¡‘  3 pE TP p 0g Vp 0 Q ‘g p 0 — ‘g Y ‘ ‘ P f t X Q 0 ‘ 0 Q — g % 3 “  3 “  3 §3 g § ¥ ¨ ©¨¦d s s t   s ‘ ” p žs“ s % 7e ‘ p t s b % A  ( %  % ”€ p 06 X p BtRiP g U tgP 7ˆxwX D ’ ˆg aUp aˆg ‚@¥)X i" T V‘ s‘ p 0 g E p P Tg pE g ‘ tpT C V QT ˆU”)X Gg €R…` ¡”aTY s¢ @ H ©§ ‘ g ¨¥ d ’  ” )sp ©§ g  d “ d g ¨¥ d t s t s % ! % ! % g ‘Vp £ € p £ ‘ Vp € ’ s ‘p B 7e % ! ( ‘ p 7e  ” € p g r % t A„ƒ € £ ¡‚ b s ‘ h ‘ c % t As  € ƒ” h r b ” 2 c % g ‚ 2 c % 2 % ‚ c g 2 c %% 2 % % % )‚ ¢ % % g d g 2 P 2 YTt Q ¢‚ WT #p “’”ip ©— d % )“ % 2 g %% 2 ”qP ¤ sT Q % t A„ƒ € £ c g c g % ¢ –“ghRX WC ˆ‚` b s ‘ U • ‘ ’ P Tg p f V g P Y 66X ` X QV QT ` p 0 QT V ‘ V ‘ XP Y 66X p 0g X 0 pgT T ” ‘T ‡X 1p rp 7t©ˆP €u2s€‚@g wCat©WaTˆg ˆr“pRp Vt€‚@)g S@g qwV iatY B ©§ “ d g % d g ¨¥ d  d sT 2 `pP ftX s t   d WˆyPlRi‚iWRp €WX tg Vptp p ˆ…rxRiP D iP v dt d % )‚ “ % 2 g % % 2 ¢ t 1S1u y ‘0 yU v dt # • U p ‘ Q V X tˆg qP aWr6 p Q i§— % 2 at‘ –“g1†T Rp 8WSe‚WT W22 sV at‘ –“g1†T R”§WvXˆg aV‘ ‚f # Tt • ‘6 Y ’ YXV8 Pf `VX  QT • ‘6 Yp’ Y ‘ ‘ P Qrgtp g t s T gpE6 T h †gxriP T ERp ”r6 1W†qP t‘ g % 2 it Wj@2 wj— % "@ d rr‚Y aY21p ¢ T YX — ` VX ¢— `pp V ‘ Q U †‚ D pg q…ƒ 8 3 43 2 0 ' %#        ©§ ¥ £ ¡ ¤5765!1)(&$"!¨¨¦¤¢  ›˜˜ žœš™˜ ¢ € d ‚ ¢ g §3 v wg ¡ ¡ % 3 ¢ ‚ p g %3 ¢ p ‚ “ 3 ¢ d ‚  g %3 P wT ‘ g d § ¥ p6 V 0 —r gP sT 1©rp‚¡B£4 xwX D WˆPy2 % d g ©¨¦d g X 2 g xWˆg 7p žX q‚@§3T D ˆ‚@B‡X •PT 6 5 Pg p 0g 2 Tg p 0g g • ‘6 Y p0 –“g1†T Rp”’ ‚@gyh ‘ g  2 ‡XSq€qw2• Q 3 WT ‰”“’”i7WX % 3 ¢ % “ 3  2 g d x2‰ g 0g pgT P 2 p YTt ` V pt U ’ D q…ƒ pg QPp 0gpCT R1‚@1Wtˆg tq1p Pf 7GRg©‚0qg `WX rp‚@g — aYwX lˆ2r”)X Ug F¡”aTY wh”T e–ˆg P 4 s V T Q p ` V 0 Y 2 Tg tpE g ‘ C V QT 0 g f ` V 8 T p ’RS0 sVp ¡— ©¨¥ d ˆg g p”PTˆg yT ˆg g c¡”aTY sh”Frq‚”C 8 g f 5 p ¢ X QT Q § T C E T ‘ C V QT 0 g fT `pP f t ¨ P wX ‚qFaV€g ”6 qP ‚@Bat‘ ¡”aTY s¢ s( ‘ p 0g ‘ pE T p 0g C V QT @ t ’ ” €  §3 g t„£ € ” ˆt©u € ‚ ‰‘ g % 3  “ ” “ t tc £ € ” g % „ƒ‘ €  € ƒ£” ” c c t tb s ‘ % ‡A„ƒ € £ c t b © € ƒ” c ‘ s ” “ 3 “ 3 g 3 g g % ¢  t t ” d € ‚ g % % g 2 c % 2 % 3 ! t „ƒ‘ € ‚ s ‘ t © € ” s % ” u € ‚ g t t Ac‘ € b s g ! t A„ ƒ‘ € b s ‘ ‚ t As b ‘ ž” c €  ¢ g ” ƒ” g 3 2 c 2   U 3 ¢ “ f 2 ¡b 2 g pt Tt xf i—  d ”qyP2 sT "  # #  © § ¥ ' % ¡ ¦¥ !$ 3 ¡ $&¨¦ ¤£( ¢  ›˜˜ žœ™š˜ Q t £ Q „7 h£ p g t “ ’ £ €  et ’ ” €  g !§  ¤ '3  PT " &" We— )&%(#3 “ '%$#3 g !§  ¤ 3 Bsš6h xwX D ‘V ”T p s ˆ‚@g WX £4 |xwX D ‘V gP ` V f 2 ‘g p 0 ` V r h gP  U r ` V f 2 ‘ p 0 2 s f p 0g t Vp 0g ‘X p 0 WeT#p asˆg ‚@g tT it ‚q2g f 5 R‚@€at‘ P w„‚@g aV‘ p ‘s rWX wˆg ‚1y gY gT p0 Qr6 g †w1iP X D ”qP 2 ”q”˜‚@g sT ` V fTPC p 0 T g …ƒœCr‚0 cas‚G7s ‚@g ”qP 2 Y WeXYˆg r”)X G ‘g p asˆg ‚@ygh 3 i1‚‰Q g0 ‘p sf ‘CX p0 sT Y 2 T tpE g ‘ p 0  pPp 0 ˆ ¥3 g   ‘ ƒ € £ c t cp % 0 £ ˆ — s  ’ „‘ ‹c £ c t % t ‚ ’ £ €  g 0„£ € d£  g 3 ‘ % t b s ƒ € £ c r s  ’ h –„‘ Fc ©‚ ¢ g ¡ ¡ b s ‘ % t A„ƒ € £ s  ’ c‘ ec g ¢ ¡ g §3 — T ¡jƒ ¡ ¡ c g c g ¢ ©§ © § ¦¤¢ ‘ g ¨¥ d c ¨¨£¥£¡d g d y = 0, v = ?, t = ? s Y4T  R“pStqP D X Df gpƒ v wg — pP tirp ¢ Step 3 Q 2 p 0g Tg pP f 8 p 0 Rg 7“pY ‚@„ˆq‚”C ˜‚@g ‘V V2QwG ‘t rp “’”#qP X B‡S‰Q T 0t V ‘C p p Q gX 0 — 3 WT p “Wqt ˆ€…wX ¢ P 2 ’Y T T g g V Q p V‚V O a = -g yo = ymax , vo = 0, to = 0 y  ›˜˜ #žœš™˜ 8 3 43 2 0 ' %#        ©§ ¥ £ ¡ ¤5765!1)(&$"!¨¨¦¤¢ ...
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This note was uploaded on 10/05/2009 for the course PHYS 2010 at Colorado.

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