physics c hapters 1 5
DESCRIPTION
TRANSCRIPT
P6.1
Golltec, (t5to.l-tbqz) i ltt $orrnvrqfecl cr,rr"e1h s$ rnsHon in tvr.'rftrenrrhcrr,\ {€rrr$
Fe-uohn(tG\b t??)'r ?ul conopK o$ mohc'n h1t\r
\.\ r Motlaha$ = ilns A o9 ,er objec,ts gotibion or ori€.nk$ion wilh hrng
T!Sg&l1= the p.!\ a\on1 tohic,tr an objec| moveStttn,'th} lce a Shc^rXht line .r rniqhl \oe c.r-.rved
tl Tqpus 6g H&irn'.
l. ELra'X\r- L,ne fbhirnZ.Crculc.r l'{o&ron: oUjecl fw)vinrJ dnt s\ cf'.culo-r pc*h
3. ?roje*ile l-{ohbni vbjec} movinX lhroqh t'[r- a;rLl.
[oVc."trt,rtq.t t\ohon'. thr spinnioS oF e,.n objeot .:"beo] a-r\ cr,.rcis bsginnrnl to1
HObion Drcl$c-*n'. oomjo6i\e imaa6 s\1+rro1.*n obisc.\k getih.o.n c\ qeuel.*\
oF hm9rn c,. .A'xed Potih'on tt
CAr iS s\ow.rng. down
goil.l- tt -trnM
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qrylg€nfrclted *r|. c;,. aiqt-l gcrint -+ he-\Ps vlaq. -se.9 ..e*nneqhbsS
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0 Draw lhe veloci\ vector fi@ Drc** -( ot il,e l.,p oF fp6 Orc^w a?-ii-?t = ui-t-il)
;fhis is }he rdr'rchon "$
dS R"turn h lhe or$iu\ rnohbn
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- All lhe ? hare lhe so.rrre lu$ , { o o,) , i *
bu\- eoch hos q di$frrcnt dirdlron, ? ; >r algcre\eva.rion
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ot- thc x1- lI -1, ^ lt-i.o'.., "{i Riotonl xrqxisl ro' ot- thc x1- I I -/i ^ jP-1.*'" "t R otonl x-qxis
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bcftom I i,,f lalr+6 lllarn z,eis b ot'ingmq-les
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and haiht crr$F ts crccr)erc.}ran fhe grec^fes+?
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sin-' (*'#Ya".se-) =r 0
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1'l,le *A', rrfpears on rft!.rb oF loFon"i le9+ of 2"d elpresEions, tn/hen r4ou eombine
these vetoq'hes , yri 'crrrrc.qlr' lhe A to td,. tV*1uo .
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b gno""l 9Ol- cr- h're oF h;s <-o-r. l'trra ga\ic-e- grn s,hogts 'b,r\\ets '"r.tt 3Potrt
\Nharl \he 'bu\\e-YE sp.c.A re-\crHve 1o q- Tv ccroercr cx-e-\A Slzrn4;,.ane-x{r tD +{^e- .rc,o.<\? (Vr)*- = (Vr)e. r [Vy)."- v Bulel- |rd twd fn,ni srre.
!U*j.a Y o^f t r rerch\€ to Grcond -*o^ts qri#'= 36fit " dSRr* vehicle 'llrr"o'es fr'Er'f,reldfr'v
tvr)ac Vof Bullel retahw 1o b-r =so,sr, iutru= 36o*ls v 1>
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- Clevelatcl rS etTpro\, 3AldU e eoS{_ c*y &cs,-.FL,.
rur'leS errsh a{ Chr'cogo. A pktne \eaves Chicc^jo t\1tn1lhe pit>f llrgol lo olrerk lhe utsi{-n( crvrct doedo tt
Kno,^r thqr lhg wind is h,tor^>,'n3 !o Fhe- tc>gl-h c+_ l9O rn:gh, , hlhd,.tb lhe- p\o.rrels
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6xr Eallg Slqin3 thru ttre cuir, tong j,tmPers, ,ct4cS doing 6tunt l"TFsnh obJnil ftvxl mor€S in Z- Dim€rrsiorrs vrc)er [4e, in?luutce Er
on [y C=r rarz f\ al\d nctthing e\qefngarleC-|1hq err'r Fra<.iRJa.rrc:e ,-. r\rr gtr,.$1 ,neglec-*-"g *r resis*crncre/ cr-r11 ?-jTl'le will fo\\ow |he Same pd-,g tr?tec}?nS r.r:l the- rYratherncdr'cca\ 6t^rrr o€ a F:rrabd\cL,
dsr.*tc.tr ' L9.to sle', shcr.iXhh d"wr) Cf,x=Omls' , dyE -g= {.tOmlszcrcc.eje-rcrHon iS cr,\r..:ar4S +he- scdr€- sI- q),\ goints :
t .], Y Vg'rh'ccu\ coryr?oTlf :F ve\oc-i\{F - Z/ | c\e.crec,se-s l"t , 9.8 ,',,s tu*1 aei.'rxlY
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lurieorp,l hos 5t-) O ode{Ur); lgrrr'4hI ba.ll throhJ &wnwrd t Analg\ f-am rru9 A a ly,il)}rn) U
ry" (Vr)i=-Lvi)+
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Elvo*ars of rnohbr, fit ltre gorebolic kctlectorl of a grojectiler. Xf --X; t(Vr);At ' (V^)6 =[V*); =Con$kr{,!l ' * I*oriutti) , v<x' Xf --X; ttVr);At ' tVr)q =[V*); =Con$krj.,!l ' * kor;ut'r1zl 'Verh^ote corngxrtyr\,h=\; r (vr)iAt -*qtnt)' .tv.t)t.," (v1); -tat og proierlile rnohbn=lnadpnder
t I tri.ih\e lol\oors cr- parcrbla hr"ier*0,1 \l A"l;+*'S "Jlo ctrraviq
f!' ji'31*"*.1,*Te tg*t belor^r o- ffinc\*^r rrc1tdrur1Strar$rt-\ire. haiectorl " lK-
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spe,ed '# 2o'ls. [h',^r ft'r does the cor lcr{d from tte' bcxe o$ the c\i${"y- llurlr, lrr^. \re- ,, t,Y ] , .\.rardr'J llt)lrl ,l!t:- v\.^U-L \rl -lrr.vlll
knovrn ' t*[ r, *ftthanh lhe ho-ri,zonkrJ 1y1 rct'3le rnohors gre.fn+gqndent,
);=o' X+ I - lhe.1'ne' connecferl lhrufi*e(t), ,(yr1,:1"r" r.,-,J-=St )i= It t tv1);At -)qLtt)' ) , ,),*=I;dv,); At
Ex'3.\L- Cvrarccrers hu* tV.*dAre on <x bt\ ttr-^r wirt <xg\ocle iG rts eyeerlcjrops bebw 5Onph. PrOblem: A e# aer-hbn ol c. fr"r**l overpcrss is miserrq,thrr1 dec;de.t \imp ttre brsover +he $f. (oc'ct leadkrl up to breeil< \c..s <^n X"t\,oQ 5o. BrstthT.neJrnq 67rnyh .^:lren "ii htts ilo gil, \s ths reo,s\c/gossibte?
-b!erv!- 6'na . J [Vr); =, co$e^;u, ' ' \g =\;' 'tvr)i o.'
jf ;l*f;,---\'.o* t- _1. u--rg'n ,l )^''=Qo.h)*s(a) 0= one.c"Jts{st):{nt'f;fit,=os ."gl_ ___j -l
[Vr), =io-fi " o=Art(vr); -rz"1ar)
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Qx= 0tlS" o
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Ronqe : fhe c\dOkrruce lo *helcn{tnq por'n} a,lr ralhrth ls=Ronqe : the c\iOkrruce lo *he | 3lcndtnl poir* orr ralhrth l+--o L* 0 =
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Vittrra
o =At (tu11; - !XAt)" hqs- z tegitimcrre s6\uHons' 0 ha =os <brrespondfnil to
\=o cr! bT,liil\:qrhifec-rtrg. tlicrnt- to fin"l when 1=0 c,f erd :t-k$urae'. 0 = tU1)i - 1-qAt V.,,1.. = -fu.,)" -uae'. \) = L\1)i- ZSAI ', , Wr); =;S)r
To cYrecK ${rsrrer tr,e .ltrr..\i fo.\e-oF ond \ondinq are-@ acrf,ne hetqht, tot#+$pNr)+ = (vr); -$ at tvl)+ =[z.b*ts) -Cl.r^t*)b,63s) Lvl")*'= -Z.(o'ls ,/'
re= ryt
h"0;Xu*SLt\N* . rr,,ni1e
u c\tskrnce-* \O:15'
xmo.x =tvi7$) .*r /:ISHT;Y::)$=1s
How dirhnce=-- [zq.sTt*tl
l.?-ltt '
=,bl; rnLrHo,,, Cista+.e i..1 .2'1,i5'
t,
vfx
:1
:
l ao-b
-A Foolt?c,.,tl-Pi-@kid<s t\te U.,.lt alrcrqhA- u'in thecriq tdirere'if 6t?^r{s (or tob,\ o$ 5,1s. \he, hocl i<ict<,<) lhe oc,,Jt clor^rr$ejd ql. ttre sc^ns9e,e<l,u.ttrc-t5 +he max distrrniA hecpukl of kick
l\r)i=V; co;ce
hr {6' \o*r.)^ :
-Uniftrrn Circralqr
7
Le-rrhctgetal frqc€ler-cl'tioh'.L>congtcinF
Accele_rcrhlorr d ;if$n.at.*q{r pofrrE**rs pofrrr A[,,.E$L A?
twd'ttie c-enlct- h..c Llrp Srrrn,Yrcrs lherEc^r.ne
I ; ' : I , i. "
.
ot |he crcte filn i" $ncirndl'r\on dfcrqrc
I;n e lnlqvc,l il lufes
:::_PGr'l
';: ri lliill #';
.],ii-lr rtiliiis-gseds b,rhi crfnti**rs\l ChCnoing dire.iionjttrill'
lfj,,,il,li'': -l ! - :i:l
tu qo c^round:cr circle ,1 |ime- \r' i
6x'. 3.\9-An crudio CD <pios eb + $cequexre.1 .$ ug to-,5!Loi.V*., A! 6'{o rjemr how rnvo\rfirn<tslequiredbronergvolufion:oF!\eoo3 ,j ,r .i *i ,---,., ..r
WnglehnX 1 reol.rh'on (E)T= r
-EHH[^-{$TL*d; "'-J"ill
iIiii
tt,*je-.u,"jj' I
q{-llglsrb ) - r. -au>o.ngr,rloronits I . ; i i .
fequired lor one rgvolufion :oF !\g=, cDl - \ ' i *i,o- , *_. -',
r tsrr rero\uhors*}1ti1li.B. = 9.o $ =t.os-t 1.-- 9 T-.t'os-t l=o'lts
y = $lg-?;m ^ (9o sacoods
" i i i . ' , 1 , 1
t't ,; s Z'rrr: ^fi"q\e rne<,.q;red .ctoct**ite O*.r., ot".\e = ?1 = lf = Zni nFrori Lt) x-qxf5 hcrt L-) vcrrpe ; --' --'-l- I i i i i- t 'P'e-Y = 36O-= Zrt- rcrcl
p6c; \erns i'&;'J;]slil"t'HJ* it *,.ia,= t,r*r*# = ,Vtr._rv.vvswr Sr A
, a\ L+l X-crxrS L rcrcl = BJ. b.\d'' *boi S r ":" , : ' i : - , i
.x eLpaie'ns)=? : : , . : i ; i
the veloofu ?is alurorlS I
Tetfxt to lfre
Cirole and i)P€.rPendra;brio a of ql\points'i r 'fisfhe
rnoli-on clfogfcrn
t{
lc"r Hohon
?\-l;o$*.\l'#:ffi
Vecfbr ooictts hwd thec.enrch oS tte-clrc)e-,
'.j- -i"----ii*--lti _L_ll
-l- -
_L __, t
-',-Ali--t----1---
-1-tl-
iI-l- j -
it-i--t-i- |-- 1
- t-Ltl
rllilrii
ii: ftt?c-ft.tt fl.o.i<.Fi\,e. r&:lle. IOW=teta- (W) -l
s : 13.J-lhe erovitrrhonol pull o$ ltre ec,tlh ori Gn objer-l Il J,C \If lu- on\q \onfl- vtrnqe to.<-e ' ' Bcr'll aD i.-r I r g-$ *t
;a *"I1$b:HsilToto. a,\ w11s so i nts "#3ri5JE''# i'Ht(NoT-lhesGrrr-e-kht,ngosmcrss* r I , , i l i i I l
f fftrfflt:A trffi - , 4 sheto!.ed 6pri,B.x:.5 _1.p*\tt $orce
ry,.*- \@o."*,.,-*=,-6@ci) :r i j,i ]l
- When a strfng <r roge or wile- p*lls gn o4 o\i9ch, exert\ contl{ Srcc
- Dtre-\r'on g,S-Hn<- 9<nSdon &r."e iS iqtqo+fS rn Fhe. cl(cec-h'on oG'*he ehrin3 or ropQ.
Atomdc rnocle-l : fiD urrler-E!^nol lhe behoyrs r ,pr,qper,treS o0 F{e{.ros.cF\c- "bj?"JFrope ma-c\e oS of-omS 3oine<l {oge*her q rooterdtc{ boncLS-a \it<e. ho5 syr\'\S
p\tr'n3 on the, errcls oF a "h"3 or roPe skre-tc-heg t''lne- molecrflcrr eprrnns .
Lu""to srg6\ -? feltsion ,l'iin +t* rope ct-r'rd ferrgicrir"r e:rPerc"ttl=.r\t - ,
obyc-t- ..r fti" dtl oF *e r-oge t*5. lhe ne-} sgring iG"r-e. berng -'*.rUeot ,
bi billionsrbillio,salf picroscog,c6err:np[, ; , i . . i , ;
pressflg crgoins+ *t e s.sfuc€- Direc-trin L perper*\icu\qri- lno S.rg *.^-e$q. (l'-) , .
the compresseo\ mo\ecr.rlo,r Vn' -Ilne sur{r^c-e-" g.rshes oo\suSfrio$S ih ffto wo\l lcreES \{r..-- A o.3crinsr tshe 'bo*'orn oF {{rult*t,,.a aqurnst-t.. vr^nt \f _*Jil:.r!,o. ts J- ke' *,e{;
,-2'iti,i,',i 'iti/= \\l-sp./ , , i r I j : ; r , i i i I
bcrsic Cpntt.^C-F Sbrcesrl#:'-t-l l 1i',i li ii
- &.,{s bcrstc c-ontt-rc} qbrces
IPush(\rih*,c-o.npressed) ori pu\\(Wn"shelched)I 1 i , . i
+- L' i
l;
i;i;irll
ONlornr".l hrce (il) :-Mvrw\r./:ili ,li il- 6r.e- e.xe-rtecl b5 cr aurRr<-e- tthe. e.rtu,t) agcr.in8t on ob3ec# tlncrlr is
It-_I
I
If'*l
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iI*r'--"i
I--iI
ll i*j-i--iltlit-f-.1--"-iir-l--ii*r"*I-i-*l-'i--l-ll-i-*-r-!i--l--r---L-1._llll-
ilii._t,_,.,!--_l
lii
fr
^")lIti
llili._t:1_L
l-i--,-itif - -]-*--t-'-itl-
:t, ii', i
.: ,, lli,r iiliq,slVrlhcttto, Erc€sPe? , i ; i . ] , i : I
-,,rrrl-,]'til,l
illl-An oui.cr puN.d,w,iH^ e^ c.onstorr" f"t& *.t;.tiwi,ffr,o
'c,astont,0ryt",fl'--,fhel'nc*=-i..]r-.t'g)n (s dire.c,t\1 :9"ogo.ftonq,-\ 1". +tte 6f?e oF.tt+ C',I1E.F-
li ,l
- Acc-e-\erc\hbn \s \nve-rse\,3 grogortrbrcrl to the fiurnber of btocXS
hcrelerc^*r'on7 d irecttltt',ro.tl to tte
:,r,i:iii:iil,riiii,:lillir i 1 , , . : ) i ', : PcaiqiI1 i;lIri.l, .t.t
Inver5q)g,
$ bcrrrds,ot = B.:.,
a i B\oc.K.- iC{=o,r
' A a..e--\'= T . n(co'neno
1(r Bbcrs) =ffi.r.p'4
Vg\Ocetr,(-V y6r..6- \r'me C;rY€^ph
Btocrk gutlecl ta1 L,L,+nA 3rubtoe,.- bc^r.rclS
2 B\oarg, - l$ ra is in*eroelta61 =tcll Proporh't(g.l to x,+heF
llis ;tin€ yedhor
ue$ord,] pnliil
2- bc-ridsa1;a ?$i i
t b"^nc\ i
O=C\r
*,' "lnertrlep', Ts.rnaenlr.t:
o$i on objec}:h>
lhe lolcrct< tS 6ec^sucec) +-
iii
Mcrts
- hhen c,. rubber bc^n<>\
-!he crcce.\erc.h'cnr o{,Cfn Untcno\fn {)1&-bS
i\ s ctct*-lerc-l$ron bf.rqJ< ? ,irr
fit= \ \<.q x O,r-:t
C^
ftlsz5.c>i'1"'
EQ= i. ocre)eruh'on=ffi
An objecllo{, rhcra6 trn) aubjec-t.c! tr'Wi\\ Urplevqo cr.n qcLelerc*fr'on d't.Jr-.?
:> F""r(-)\= maurn oS ou.r-t tarce$ 9-h,litvr Vhe 6c{rne dirir}r'on cr-i
R* = fi]'d (s"rne- o', '
where-
i:
ri
-Acceterq\bn iS lnverse\1 Progorhirnerl
:Hcresi= +he proge.r\ o} qAccelevcr.tes i n r€Eloonsg
i S 6tr-e-+-c\ed tr5 gv\\ , <an cr
fs gurfrecJ url {.lne- €clme robbexts S,Ohls3. Whcrbi ++re, mcr$s
riliclnstlr-nf Sr<cr. b!o"J< piV
hiSq-rie brc-e-r:
_E- Direc-hcll og ltieqcs.ler.h,Iffi- rF r'!re, sc^Iae-i cr$ tVre
*' .i ' .-dtreeitrn r oF +h- q-..e.
7: j l
2.{6,l
i
I
'c-\e-- Reprcaerhbs +he, .Fje'+ ic"s, cri ?r.+ocf n3 en the- 4-;+. i i i
,
;€horx$l'i
Ltr\e^rotor .iS crcre.lenoh'cxq
I t fn.tli
ritt
i::1 ti
ft;,9rY' r , . , | ' r
f) rt
i,ettlltjri
lrilirl
oralclrt{'ll i1riiitiii
I
'1
I
I
Iil
I'.I
I
Ql
tu.- .,f the
:ir- B"Utor.,1 Sln4pSicr SrnrJf, rnpetet rc-f<e.f, b g. bt".fi( oS , tcg. .a"46h6crk\ i| erross *{n. smc,e>rln aurftrc-e. of e. 0rc2.r, .[q-l€,.i Ft'chon ts nel,lrglbte--, Dro.w rco. l,:puc*t cr,vervicl,w,- moh:.oyr
::
C\togro-r., y to..q. fdenhiG'cc+r:on cltoq,rc-sn, <trrc} €tee--1U*
nar'md;t€dlfF
-, -r i6phl' i t-zi
l-u-| -? t->
fqh"fa-i-'_ r*r-*-l-.
t-i Iii[--L*-j--r-i I Ph..'-.ri!*-r
I
----J---
l-ji-i
-jI
i
7
Tizrrnino\, tPeecl (Vo"'*)ff r;r irt riL?Spc.-cl :aF.llrtc.ln Hne
_e.ra.r* bc^.fqnc.e.,b\ro the- up.^:cryrc\ 4"1t S".ig Grfl+lne- downnrc^r,C we^tht fur.*t ccr\LBea c.1 objec-l b $<-\]\ w\<.r olituSc'No"l
-)Onc4 6,g1 ob\ec-t hcls qecrcln Vte.rtrt, 'tlr wt\\ con\*nv€ fc^,r\inq -* l
lhatspeeet t-vtlr\ &hitslheg**-A, . ' . - "o -
l ]
@ a , Iy.*q' x A heevr'er objer-l.hos'o lorger l-errnfrrcr.l tgeed-+{rarrVrerrn ='.1 i;{* R a. lrghter oUte+t -g+ ?q* Efee x
o)A* low speeds D ,'r, fti (to-ridr'crfnefer ep ,ol ryross:eo1 hc.s Vterno *lgh{slA* |ow gpe-eds D rZ, ffi (to-ti-d,'crrnetbr q,p dl rlross=""a1lt"s Vternn elgn( ,
r's srt+t\ e^srct +he \r/ la7f _
Whi\e l0crn-dr'crrvrerer lerdbott w:lrt*r.=6 q hcrt Vrer-'l€oqlbc.$ f-otlt ,-rl q =S U J iP Ex 5.\3., Terrntcrc.l epeeds a$ c^ skq$tver arncl ec Hcr,lt
b) ns v rncrecrs< sa . > .
c{e-s D. Thene-} 6rvc. l" lr"Y-, ,{-1>--t"3 ,--i,g3f *Zos v+*'wr=lrl@anct henc,e- o s*t srr,*tter + t %S
e-i- -i. , # :
., ',l [ffi'.uc)6r"",tt*.ttX, V recrctre\ c\ vcilue l"r=S) '
Srxh'ltct D =W. ttev, 6.; =6 J ;S qsrxh'ltct D =w. tt'evr Rel- =o .1, -:.f frt Vt*r. = .'1 (\.21 7-" )kr,iz,F) ih;
r r ' '1 :etnii , Vrcrn = \J -lsirr,t.t>r , l
ond the bqlr falh crt aconttuf " trn"+=E V.-r...= SG hls6pe€d
Lr if !o covne !o a s&op r,nce- tk 5;b96 €trfi'y6ryriq.D = 6rr (o,o9^r s'l/''.\zbxrdqtn)(o.zsx rg't ""t-s)D =t.Z*lo-'oN
tt Sc'.me rO\eqS c'-tp\.1 to o\ecle movinX horieontcr..[\.1. cr\eett, bh*l^. of Shot,honaontt-l*S, S caDscs ab)ec-lr b s\ow cfow . Terrnir,c.t sgead Whe-n D = F+n.rr$F.e.t ao , obje-cl c.cr{rno\ to q^t{ ft-st q . , , ,
bO.la b \,'"\ulc)s Viscoei\(m.c^tn re of ho.-s mucfn reeistrrn5 $.$\o,^> {lrre $\uict brcli
i=(tolqrv, direchbn oggoeite. ho rnohc,n) q=viscoc.i\ o* the-hquhl'Dnag $cl.c-e. rin \iqurd c{e4err15 Lr'nec^r-I1 on thq epes.d
- Por..melrrr. = 6f$e-ce.trecl cr4drncd <r.to\e fo grogo\ i\e,lt ciutcf\ *\r,.^, $l-e{ ir6(nX tbtr ciL.,Trlptccr-\ pcrcrrnecivrrn hc.t dr'cr.rnefer oF 5A*trtl. Whcct's Hn<" clrol S'o.-e- .rn ti sr*iirnrrr
c..\ or spo-d oS o,es-^lsl lg its rh4ss ts 1.ox1cir \<3, eskrneli ha^, lor.rq t\ bcAres-) Etcr_€
F.roo.l\sion " Port^rtr..ivvn covret to cr . t = zxro-ss = 2cr;.rsf , -_ -{-$ ho.r.r\v qlrnos! inskrrrloneoosll ,cv-- <"nnr '&'ffi'tTi'S,.HJti{:q ,.,tffi:i ;g;tT;3ftotvnni5 ctrirecHl \aroFortr'snrJ . ] \'
t"Ju,n** o*"ee it starts r
;!t t\e- prSgrr\tton [.s..q ;_ , i i l';jJH'silI^5"GJ;-'= ,
D is equo"\ ond opgostle Fsropu\st'on
otlce ft stof6 Eu)trrrmrlrc( C;t=H= i-r > rro-ldl) J
,rc.e it atoeo ,
-\'2-x(o-rdN'c\=^-ffi6T8 1.,1211."i-.rlzs .usf:lt: .
O=5EAV - Av _€_._2.5^to -1:-fr At = A, -t2-mf6a
tY.l
ttt- f- -1 --'f-
I Fcll l
:t_I I
-lr-lt-1-l
i
7t
Arod .t) 56reb+dffi
Hon\ 551tScr&^se-
rhg.bs oF lE6o
o-ts cl 20'aalg\e-.l-en.,lo.l tn, the
I
, Thei
I ''1hql'
-A fic€-Lc,bhortt.tnt-ft3aruX Srce scls
, ,* thnts|. l-
Prtoh13\1rr-wn
Wo Sebsr6-zzoo\F*."ei i \,-\ocpr\),
D = !OO-t*t
[o:n d 6zoU opp.6"s l.he
trorn reEt tD lZh4b in 2F*= {* nT.asOF rn'g1x i
I f.1-, i
,)(."owi-.. [V$'o'lt. (V,*,'tzns
At = lo5
lftSzou ,
rn=t5tokq
0 =20' \'
T.-;g.-f*;IYl'Qy . : :
a- =ff =1 t.zt4"'Tlq5o(zeJ=i l'lt") r 3?+N
l
WeiEI.t, noh
ft
rli::i
hfriCnSoeAiiiijri1rlii1:l;iiliiiiillritii
illiil
rliiliilli.rll,"r'j
SP tl n3 qcr*les nneq,sore
crsp
+ Spnnq-?u$heS uF(
'.5t Bp I
r..5, . -r: i
trlre;r =O i,vg-werd 6pnng
. rnutst e-xerel-{i{'bcr$ge the
-downwcrrd weiXhtft>rce. :
FsP" W=g '3lil
iF-,+, Fnel
-A cr.r1l wiHnt c^r mc*ss oF
When d--A , F',<'r= 6
: rnovrnq Ooi^ru, Wl cl (-): ve\o.i\ rt: ll: :
;;
Wet$ht\etsnessr\e\qntte\sne.b\ i ; ,
. -n'"-"hec! thlt r's v{etS\tless hos no Agg.rent wetXht (W"1e1=q) ,
:ItT' .^: 3ril : -* l=--x' .1:-::j"::, 3* rltl T" i"l**-.T'=oJ: ', ' " : -'_r *J ' -'--' --J.: ;- | l_^.1 , -l- i'-- --:
Perrorr's u1=tY!-fl rerncring true. Weqht \Clt' ng e,$$9,r+ c*n frcr.e.lersrhon (\J , , , \' i : i : I : - -f--,:l'li
'.'illiiwetXh\$w"r"i=o,) , i,) ftrll qull. Hne ;6c".rng cl<+-e,f-elce$r
Si -nq .,$$g.+ c*n crcre.f€r:srh'on (or.::iliiii',jl:iil',I,ijiiii.i,j,iIri
':.1't',it...-
- !utl*, +t ncljstq ilse\$ eo tslnc'b t{"e.' oblec* lstuqs ,o^. h.
ISurftrre=wlt>genehoh\i|. ; i i , I
I
E -a... . r' : , r
.,liri6 S3: ruorrncrt [n"q.e-gn a p**.cl bolK -' . i i
' ,l t . ?- ka h^.rla li.s., ^^ 5. \-\p nl-Lo l-^.{V r's ^A R{--li15,1: Norrncu ror(€- 0n 4 pre88ecl bodY< | i
: ,.. t1 ?1.* riesl on.
.,:rrlll'ililiHne. norrntrl fuf.ei crdn'i.X; .n t"h-
xQ. N,cr.
fi.l+olibliil
ilt
Z Fy;= h.1 " WJ t trl = f\ -iW1F=A _ l_ *; _ ! i.w=F\ f}:iY!rE--i.-. -, f-,-
wu {1..i*X1,8'f") n :-i!aN-I ;t5r$ i ,-
iir<t\lrtlDLN I l
BrJ-i- l--l '-itr.l:l:*l*- t- i--- - " i--'*l,lif .i--i -'-'-';'*,'
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On <r{\ [nc[,]:Oe.l
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objsc-l'-l
4-t^ ,
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ll ;Yi r I :-i^hcrrrno-\ k!,rc4-
c*\urcrqs ipc"int'5 l
p€rp€ridier&\rlr-r hJb e,rorEfrr€
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o
frr
- A skie,r- a\tdes I c\own6r\ow. Whc.,,t is hiS
Y
i+
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I
lliillili,iiiii1irs\idel'--tbc,x isFr= l,tIt
n€€
I
l
la
mov
G>,deturrr.nsrh'qn ot. r c\
f-tr =4r- f\ a4r --
Dtreclf65,r1 et f, r O-ggosr'nX- Ac.rte Ve{q sfrnitc.-rr + t*
Vcr-\ues oQ l{*. .; hJh.1
:y: F =(,-ot"itua;. t:* = ,"i'ni :1t".*..,lurn#*ri iiKinehc-l$* *,(^^r.r1 r oUrec-h'on opgoqite- thq snotrbn)
Ro\tingl?.=(*..n,drrech'on.*gr*,t-+^g*"1.".O ' i I I I .
.,.O t$
9b1ect ,1 too! rnovinq re-\crhive to theetrrlrrc-e. iY'a tn conlc.dr wtHn{-trNrn Sor.-e- = Sk^*tt $ctc-}r'on ,
(D l$ l+. o\1ech iS s\rdtnq sslc.ttve hD
= Agrr$
i,ltcl.ot<3 wocc\ box ac.ross a c+h $^does doro\ erer\ on the, bo:r ( '
rrliijii_]
: F =F"a h,t f.'.^j {Lei nortnc^\ gerc.e, {*ir*.r, gives t\d. rnogw
:ts (3 Ro\\ine. . c--\ons the- surRtr-e- . P.o\\i.'- E.'.h:r'h is eoatn'no i
gSi"l 2 ft--FFE\ +o h',"ci H"e normd Cprc.e., f,r1l.rr..h gives t\e rnogt\9 o{ecJF (s Ro\\inX, cr\onq the- surR'r-e, , p.o\\inq Ft.h'on. is crcJnrr
I
-r ^. -r c" - .. *o * c, r r-,-^'.^^^ ^.-,i ,^'-.'i- 'i - --'-.J'
'F.a n alnd u6e $r=Ac.n- to R.".f :Hn-i.ry-,tl-@ i i ' i i
-Cil511\ prl6lnes s*h,l *., m$cl^ tr>rc-e- :.{,
- Bc>x rhovin3 c.rg e. crrnskc.'rrt :6pgsc\, 6<> Fy1*t*f ,
1tr^=F--Ss:o CK=.r{r<.y'\ Yl=w=m.t' , r i j-*=o,z(Somt-ni.+.D, 1E-a
-- '
I -T6aAtr-f\=*4ntYrg . i
= (o,eoiir".o,.t> ,i. t**p o Z,o*
iiiE r.ie C:.c^ro\i
"q"+ h .rpp\r{ h,
tq Ka"+ il- grovinq crt 1ot s\ecalq
riit\e" box
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,]l- L<r,.on ro\\ev iS 6. [q6*lr5 1$tncler u6ec\
ts t+ ecrsier l-a gush -. p,,J\ =L.,1^ er rcr\lerl$tc^r+exri.q Fl',e- tcrsnl po8hrnq or putlinq?posr+ f" 0"""__.,:ft't FFg5-t+;\tF..r.E[n ' fr.*=a l*q,
'lf lhe horrncr,l $orc-e th') of fhe qrourrd sn the
1{6:O.t'Oa,'lh=0.60
eok3
fi'.d- ,
$s lrrhen €=2.c)'g crt ra.n*'qJv., cobireb
6lies
rdler is lorgel bq Netlon's 3"d lcrw the $rce o$
l4,e rolter on theqround will Ue lo,,'Xrr aS we\l
Pu&trr.Na = ffiore eFd-tiu" fr, gtoUrenind 1*r torsn
ftt -g. \Z'. hors tu D.^nF,^ E Ie. c"'\-t^et- A 5o.o kq stee\ Rte. cc^Unei is r'n il4e bf{rX of a 'dump huc,ts: The trucxtsstee\, isJsro^rf J-lt€ol. Whu,tklh..iee of fhe {s on f+. ."^b;;"F -i"-.hltert 20' i A+- v.Iho.f anq\g oill the $ E c.,t-,hiF be*,rr to e\de- |.U.\ll<nc.,,^m F te c.c"Sinek uri\\ a\ig whrn $s recrrL,Ls $s,"*,o
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bd ,cJEo qnc.cte o€
thq becl r'5' l
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e!* it a\ipe, $1\e ec'bine.i\ tn Sk'h'cequftlbrrriln2e^:-Ll-)" t w8in0 =o zF.f = (tt - rN.c-oso -6
lrySinO - (R) *, =Q 2trJ = n- Wc-osetng sine -Ss - o L- = fl- mqcosq =o
f "
-" (& o q1l g' k-) s tn ciD t s = .'.. glsi ne R "i PSt-
rej '65-.*,.rx =rAe.n =4s*{"*,\q"r. =t.r.shqcos€
,
qs= S. = tcrne t> = tcrxr-tAsc.o6e O = 3ol.
rr,liii
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'ln.,rc.r,*esr n clirech'on lotn rnrrcgvribcle
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vg\ocrtrr trt
the abjer.hts speerll\ne,CrB
Dt $ t.,, R... ^/i?,\ "wa.-Hode\ o$ ctrc,,X can be uterl tS {de- Q616*r'nX 3 csn4fnUns q-(e. met\ 0!$ i\''[he abje.*t eia,e L11or.sy.r) fS bl\N * $.,i t-nnn sn"\ + {=^ r m"r.rs X efB- -
' 0\ec-td =g.*O is \ess thc'n c* $e^ hvndred '*i* ,
" ' ClUSec;rb ts nnovinX throulh th1 c'-ir in""* Se- eorthb ptrrg.+g . ; r i t,
A = l-he- c-(rrGs- seclioy\ crr€cr of ttre- oh-[ec* (i" r.tlD=' --tpAv' ;il;H;=;;i.il,-?;i Jl;*' \rn I.
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x'[lneeiee- o$ l\e- dtc..t torce in oir is grogorNCIr\cJ h> the Square oC Hneo\ec* sg<cd, \+ spe-e"d doubreJ C"ltsl, Dra{ *.**'b"1 fr"*roT for to)
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tOt<3 b\ocx 8., th. ZtUr".f.S rraove- ko3elh€r. Whouts Scce, eJoe-S 1o1ogt< A .".;*lo K3 b\ocx B ; tt'ra z b\i<-Ns vneve rotett*.r, Wrhouh tbrcr' doe--s b\oc,i[< A .".Fdfon lotsg\_-Bl nter f r5p"x fr "'5F= (F*)^ *(Fso,.*)" = fra.o^*
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as orre- 1.merngqi rg f"^' T5q.*l r1"^+htm;q^'r o$
T1're- L ynervrt",.r.s oF lihe- gc^r'r c,.\trro-r.{S crclr qr:\ Di$Gefer\+ oblecfs. . i i .i i I I r I nI ,- Tlne- L rnernb.erS aF c1..g\ c^c-h'or./rec13lntann f Aif gern* in oggoa i}.e.
lhJ=€lercrh'on Constnain\s,Ac;ag-_ cc,{, pu\ting c' loox , i t-?l-=PheurtJ
tSkGP ynss! ho,ve e{uo.l Hc,nnihd- .:F I l-stsrto1
-? *li ;;'.+";. tu* i
Ets qEd- "'= F"xJdi;s'lt* ..*,t A pur\s diregrl on Bnl" fi6rces on ecrcln b\ocK Gf\ B rout\6 c\irecHq 6,n fi | :
"ks#',,ffi,iflfrE hcr've-*t, I tBrocrs ar-ts tiketh",{'€i*,5.,|!1fr^t . .
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TLnS,ton = Erce- exertecl On cr-n oble-c-b bq e. f.oFF , or sihrf",3t i I I ;(6,*r)*=O irng\ies'Tlioe.anrr=f,."r.".*j I f , i i 'i I , 1 . ,
L> I?re ,fens;crn fn a sh$'cenc.r1 rope- :e-rts ertqc*-t\ h+nA G$ bol-ln i*-, of \he- r.,pe. on v{hc^b+; obiec,ts th.l ropq is ++C++ai t
i
Hcredesu roPe (or shricrc) aggrorirn*i.,. = tenqr'on t,s thq go"he ,ttrturXt*ot lhe
-tlt" -gr , I -T Top= ts "^..rge.roSn1 b lc- i9 fJ\c-pe-: 9, ll6er)= l'h.o*l-4x =O1
LB\ooKs eonnec-Fedbqrcn o : t j i , I ia- lOfoC/I\- ggr\rlwlgtl 9Y s
l:f -? 6rrrn3lA\-l tsl_FH :II$r!"^lo-ii+r.'e-sYrr.5r5 i , i , , i , I i is '? we Crt6ume iK; -r t\
lla- TslTl - rn4tss\ess ^ : i
Hrerr> boHn ls\octS. I I The. 1_<ewqanenl;t e t A pusltini b:r. s$,, <rc<-e\elr^+rr,ns 1l-;1 f ;f .i eb l^".-to".rgt# Scrrng cr.c<-ere-rcrtlov\ cN"- e€tucA I I l5l I qg r.s c[cr.-*r..>e.-r€[,cta=a.cs 6\eo. -- -A by I -
{ - r,...* .I)-- ''
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ta =s.Oxr -qkh.on/rerrchbn pOr ht4 crUi"=61** *";'u'iffi"ii;J.*'"'' ti. -Foo^[$:YY\n'4x (Cl\*= mts ?
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Terfg'ion = tgOt*f i
eqvet, hrl *r.oXnituae, leF,
Grc,e- atg\rec) (toors)
P,,r\te^rc-
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b)
- {he "h\ *^+ lhe putteq are- both r.rc-rs\e,ss
- There i s n., Si-Hcln wher<- Hne. pur,\\ h-rrns
tl'llntran on Hnefl 6Frinc" r's *reH o?*i s.n-o bot-lrr aic[e-S
oT vh,c- 1or*ttc!on itS trx\e I
l
lhen no he} for.e lE n€edqJ to acr,eterc*e
the shinX cr. l-urn ,Ihel putto.l
"l*vr tde.cd r.q\le.r.r6-\61r,qes Vhe Atrecr,Lntn whicfn a lenEic.rn
*:l?nsicrn fn cr, rylcraslets slrinX rernoins <onstcrnt
as i| poEEeE over a- nrc.eslessr Frrch'onbsslpullcl,
- A 2.oo ka Je\ rrsed 0n cr ptcr1 f S slorecl in bhe I"Ft obove [.he] sh'oX;, Tte- r6pq ha\cl,r.. i (Jl
{he- se} ger-es.S uF e av"xcr pulterl , theq t'S hed boc-retcq,-,, ft. air.i-.fi"r L<1ts ".,
fqf,,e\aryhond to tto,rrer fhe se|. As he. urrh'es *re. rrX'e, lhe gef .fiilK qrrd the nnor:r fs
!g5|"{_ltq fhe tof+, whotk the stcar+{^rd$ cr*deryAonlI
ii
ffi-- tsnsrllro- o..,,h* is rncrss\egS cgret 2pn) = T.r4- Wn=Trr- mor1 = M{o*^\d;l l;t-, *:lrs.. lffi*s*as{ lt irj*'=Ts- wso rs-\y1s3I ''"q"r
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$l+. Hq., -*? -1 = ::x";=?:,';
necd<cr
Fi.ncl : + l-- , :T-fF=B=-rirl-.iCtm1, I i ,
ili:lffi= 6\c"--dsr v 11"' rl*"*t*.s = -ii" o_r'-'
, 6' F-"r- | r *"qjdl1ftfJ*m.la"1='4d aut *, , I n* hT=:[n" -u=r%,".rn.),3 = -G{.l$ak z
S"1.t. *K, br.rt no| rnasrritude.'9i
]lt:!t,
i:
i\si
s
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\, :vwia flrrA*\ 'tttnt -ffi" $= -fhsC(*."1stcqphcrncl's upur--rrot ot 0tu-lytu)g,=i*+ tnn..)o rnr
-skqshonclk upurr,nd a (n" - tl1 u) n = intq, *n^..J Cl *.rDorrrn'oorrJ a ot bus1r"\ o,...1=$t-t/*= "yl) j = @'{.t\r,, ^1..,--" -- -,-" *i'1 -.,-,
,. , T.- h^ r.', : I , | | , I I ,.
-&^nt< Robberls hcrve pushecl c( t0okS tr.r$"e *o c^zqstorl \.*J\'nclor$. Pton to [.ruxr the sc'$e- 3.Orv
tu their hrucx, The^1 Etu-cx up 5oo 4 art fuy6iture, h. cL rofre- bt,*r {4re- sc,$e- u ftrnittrre ,L
plo.s,e. the rope. ow.r e f"lt"rf . 'Ihen tt*--,1 t{,Sh khe V^Se. ou} o[ t\e tsiYrrqs , trlhq1.t:+ t|'..-q
Sc.r.Ce's spe-e-c\ ,*llurr it- hibs fhe lrucx? ,.4rr {ot,^l frxnrture c.ncl Sloc>. it O,SO{:?
h ffiu*H,; *lkl, =':I ry:;lill*fi11J"\coorn conslgg\tr J,*
-- ' _'' '
1^-"=?l 13 =-_
--rxe* ou,^ o .,,' t trst =T - ftk3 ' (Yrs clsl
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