1. P6.1
Golltec, (t5to.l-tbqz) i ltt $orrnvrqfecl cr,rr"e1h s$ rnsHon in tvr.'rftrenrrhcrr, {€rrr$
Fe-uohn(tGb t??)'r ?ul conopK o$ mohc'n h1tr
. r Mo
tlaha$ = ilns A o9 ,er objec,ts gotibion or ori€.nk$ion wilh hrng
T!Sg&l1= the p.! aon1 tohic,tr an objec| moveS
tttn,'th} lce a Shc^rXht line .r rniqhl oe c.r-.rved
tl Tqpus 6g H&irn'.
l. ELra'Xr- L,ne fbhirn
Z.Crculc.r l'{o&ron: oUjecl fw)vinrJ dnt s cf'.culo-r pc*h
3. ?roje*ile l-{ohbni vbjec} movinX lhroqh t'[r- a;r
Ll.
[oVc."trt,rtq.t tohon'. thr spinnioS oF e,.n objeot .:"beo] a-r cr,.rcis bsginnrnl to1
HObion Drcl$c-*n'. oomjo6ie imaa6 s1+rro1.*n obisc.k getih.o.n c qeuel.*
oF hm9
rn c,. .A'xed Potih'on tt
CAr iS sow.rng. down
M
,-Pcrrhbe'. An obrect $h",.FcSrn he reprcserrt€d €rS q moES ..rF cr 6i(r[e- goil.l-
rrn tt -trn
L> - - '++= 6how l4rg orcler whrc]n ihe. F.rE ffgg p,Je-re- f.c^JrJn
I t Sq 6rn6g c!.of re-grqients cc*r @- erch pJn* io ttrvre.
" 6imgriS'*1.,orr whe,qg we lreaV a rncryjlrX obie+t .ls if q,tl! rhs glass wgve
qrylg€nfrclted *r|. c;,. aiqt-l gcrint -+ he-Ps vlaq. -se.9 ..e*nneqhbsS
'IqE
l'Qe-di.r.entors, or
"1-D" rnotis: obig, q{^t fYtove orrtq crlorg o sh<lr$rt i,re
i'Plsltbni ou,: o,51hb,r. cr,l o Ferlia,rkr- rnsbnt in
l. hmQ. l
l"r iee.exSce ?o'o {r'ri.,r
S1ste1]for-ilj'Csordhc}e $!4serrrt An orrgr'n curd err o,l$! mcukeelrn bolh ;== Y :: eli:eclrbnt
{9:.{'ttF i:Str.l:1, T': 1 1=1-*. OqndG) 11 -l
Dakr,ral
_ftr lhe

2. " ' * "**" **'***-* "'-j* PJ-I*L**-
tt
b 9l.rl- e-"lo<)</S
Ioe-eh tbu."d bq.ftfy(
Chotc,€. deryende sr whc^t gc^rf of t
lt:i*
Ax=

3. . X.,e
'6
lime irrles
- Tirne nYsr{c,
to0
= o,Lt
1, 31,'
,621

4. -: {.1!* ;aq;r:fglfn# qt3 q'w*;{,w
t1
____+ 6^..
Y
.F.
At
horn its it{ihs"
=.1.
rd, : lhw Auv
'4 <n
r,
Z= AL*r.,4

5. _lirn*
balt sl"
% botl c.oncrn veoo
t4gs-$s rrhe- c4rlc
= 7kL1
Scrrn0 nncrtherr,q$ccr--brO-
--
Vc,rries crt" or "depencJs on" Y "^
x
, (6"u , Udx2

7. 7l I I I i I : i I I '
-;--..-. -f--+-. -r--+.-----:---,-
-l-L I
-.i*rr--, |
-L-:- --r* l-i-
---i--.-
r LJ
llr - -
r_-j-i-
--t i$erpreSi.uqs $Lrbl
1i!
i---,,---
L*-.= i- i -:
il.4+ €=Qpirf,-
re*IEL"l.-
i-$*e]-:
"t-r,"F-W
I i,, l5i
I I ae"aoi
i
T- r--
[ ---izo i
eqlr_$b-e&-bb_ I
_-.-
l--"r
: I i_l
I iVoI-
-r -i
; lF ih.l
: '):*i:*:':
1Vgo.it,t
i i L,j,
r -1 -1"--i'
i.-
'iii 1- 1---i-
tl't't'
-t-'"*''
I trt!
- I
tl
.--!---i
tlt,l
-
i
I
ri-
idiu
lt
L-L l
rrlr
i
-.."..i-
tlc.
lLr
I
Il..l---L
I
I
L_i _0
riP
--.i--r.-*r'*
tlt
rlt
-'--1---i ---t ---
ttt
tit
rtt
-'- r .-.-T- -t'---

8. _--t--
il
I
i----l
i+
.*i--*
I

10. ----i----
i
-t-* [T
I
-
-i-i
V.L
-tfr,"
1
I
rl-

11. I ula
i
I
- 1-'
i
'--l*--
I
I
-r---
I
i
*i*-
I
I 2ft si
" t'-:-G rlS
Hpnj:_lS_
i:l
----l-.--.i.--r,
ill
--i--- j*.-t
lr-
Ii
-t
I

12. 7l
| ; x VheYh"ti ori ,,ot nn,"t* rtol|,s ar*ii,q :pa:t
',.T1" '
lhe biqn
n r, '^ , dur,*r-, flo* a. npqd^he ..i,..erer.*ho,. aarlrY*
^ :
oY Ac(€e$hbn., on nhe,trer ilre,dbio* fs ntvirq*o*he,d,tso.
i
I
Lg{.,}
I
'iu*,J,*o1n*tq}he;,:},=l.
r
oFm,-o::l/i;'='iji:i
l P"sit"e cry'
e"
IIb1-.l;=*i*r"iI ii,;,i
V,.>o ' , : ; i *j-;
-_Vi.O , :
i Ii
I . " .
"^Ng*Il*b*; .'
v^" btt*o,;novinX
tothe Pi$ht
"j_;';
,
H*,-*ri
l:"'
I
I
Nqc*h've
n{c.riv.
aop,
(^)''
' |
l- '
Neq(*live
,icqot
6oper
ug O*
i
i
:
*. ''
Htl-?r-frfq, : 1--'-prEFEdH{Fsa!' , i : i
:
&
-
Hoh'cln with
'QonskmY
Accele'Cr,hror,, i .: , i
l- ; = - I:
4L *c.,=ffi l.dqer. wbrcse cKceie-vcLhion:crx te".i.'*
Lrx contkcrnts dtrrin.r the jh.,e. tnervoi At {9 -t; I
1e,rolion {o-q
t con6l<rl$
I l*<";c,c<etergson conAk{rt-ocs-efercrhioil nlqHqn is ca ;ehc.rinhlt I : i
-t -* line-
th.^f shq.rfs e.t CV;r); i*t.l jhus utope ;ox
:
I I I
: i
Li-+r
i
. tlte't'" ib.ifrnd , , av,
.
-ti"at+
o
lc^ccelerc,trtPn q1)'j(VJ,
rffr V
(vr*+ con1!m|
iil _$*t-lu*J-"$il
,W;/, { h, ffi:ruE"1*tm di[J;e"t'w1'c-n*<,r.u q" I
I
;iI
: (uti I { -- '- +,J 6J',+';;i 'ia,Wo; , i
:i :: :
ttffi-iffiP' dtspc,,ce-rnqt i tn;h'"d'*" ouj..ts posihon Xq'
( i {t l men tiq (<nc'r^'h) .^'
,- :i I I .-
Rgc.hirrs Veocit'r o.nd
hr cr,,stii.'vF -cr.ccAerc*kbr1 rt9$-?n ,', , Xp =Xi * (Vn)r At r*a*tAtyf
*fr
i
e
W
1*"r;,t.;l.[6'ff',V xffi##"#"US?&SSf,rW

14. 71 lllilillrrll
I i i 1 r i i i i rl
r--i-l
i *f-
I
i ; j,,i:$ovino i0*u, Diu,er
t I
:'I-,ffi
: r:'! Pibur.*'i g"ptl*arr.ln t'' !
..
I
t i-j
'*,-.--l
I
r: I wrtc^r .lr*i #e b+^r lais*rf^ *-- -t-
I
I
iiiqrcr+"iiii,
I
itii;ilii;ii i l=5i
ii ,+gji
-iil'=kl
i i' n, d;*;ri i I i,
,irj,
i I i'-!:hdl""Lui"st"sn l- I I ;-
i I g.q
i: U,..t"n=+- '
* -
_ _j:t"F + tdP:_; i__l
, . : :Gr^pU+el Sge,res--e$$lon, -
- i
i *-i -l , i-;- | :-i I I ]-
,
-l- ' i -l-j - -i-i -l . -i
-l--j- -
-i
-f-
!
[r
:r-l :i -[-li-L-ri
-[[i-i*L-; 'r",.rT]
i-:-l-r-:
iFX
, i *i , ,---,-. _r_r i i: I l[f
j,
H-_[ _;
i --i -l -1
L= Kx l_
--; i-- -l r'*--t-'-'--
L-i 1l
- I -: -!-t-udr.ho.n-
i k^-s€dla$ 3, qro is,S"t
-i I i:ilfl*.TYiiif ii
i"v-e[o<
ziq i
-iFxqs',p-!ei i-- i--rryi)e-alV-0'r Ar i-
- r, Ltuo:-- aGIlsl-- *. --i --hjPls;iO"1h ilbpG
* jxipor- i-ubt=olt|s, I -k-l=zlo.$t lr i--
'-
;_ iUrca_ i[v'i+=ruoFsi t__]- i i
il
end
i I I i&thr[V']
l-' lEfsd" I.s,-j- [s {:ro@--t*
: H+
'
{IG,o
-, ->-. HP.o
; i r j l-, t r-l*:itlt-c1r
i
1i
li
i-iitii:l-1--f-i-r-l il ri-* r lx.ize'P"
llliillllillL I
..i _-***

15. 7:
I
i
t"
i
I
i-
i I i- i i 1 l' , ^ i I - ;
^;
'li1
;'l
i-;- r -_ i-'-
!
o$ec};in ft^Ii i*
l- t
+KJ
+'i
, Acr.lr
li
r{
1
,'l'tc
FqpoFioo$. Vyl , ft = -S i

16. 71
-T"-
I
-t--
,I
-.i--.-,
I
_t_
I
l
I

17. Knowr,.
q,=!oo-*. t+ ond (vqe
* =Qnn ,
tVq) i =o'ls
ti=o*
O. t= {.80
€ur
iq
.Ttrrn(nq
+ R.oeterahoun
atu,lculS =
" "-t"$'
I
l
ri
q0'.
',ri

18. !)
I
f-_l_
ri
I
I
f
I

19. .,.. .. .-
I
t *-,.
k+n. =.
(: 6
L
I
)/_
-,r

20. 7 :r
l
rii
rl
ll i
i-t
-) -)
i
Vs- V; r) ; AV'
Aaelerchbn fn
.il
- -
(
ll
- tp-tsi
, . v At
/^r t--
a
Z or morg
climenttons
ti r-.
-; .-1
*fo f,'nd +he accelerahon bl,n t/i qnd Ys b'r,tX'L': 1
0 Draw lhe veloci vector fi
;
'A spcF.ecrqh sov.rs eh ill sq$el1
@ Drc** -( ot il,e l.,p oF fp decenasi tu ltre sur&rc€.- o$ ttqrs, h
6 a?-ii-?t = ui-t-il)
Orc^w Q conpgk. mohbn olicrqrom for &,e lc
;fhis is }he rdr'rchon d
"$
k^ c
sLnas +he iecent
S R"turn h lhe or$iu rnohbn thts, rlrowt lhe .Vt
accel€ralion al t t
dtcgroxrr. Draw cx v€ctor reh
fotnt Cblyr V, e^d v;
tlc, midde Doint in the olirecttxr 6Z is to*e oir*l
o$ o?
of A.-,i I abe, ,! d'. fl,is is +jtre A?
I
&lg O@)erc.rhon cr,F the mrdpinf v'L
bl^ il; tud is
6$3 i ' ,. -vsr"ri i r li
, l
-Anng rrdeSa brrr Hrheel cr,b ,1'
o.rr vec,tors Ir;"
cmusQrnent
'-- PqrK. Drc^,w 3^nek d,oqrc.r,n I / o o,) ,/ i
fno&rOn
/
- All lhe ? hare lhe so.rrre lu$ , *
bu- eoch hos q di$frrcnt dirdlron, ? ;
{ >r ,
' {.--> algcreeva.rion
uo*tt-
Mr
So thcrrr T$eons Anne is acce,lercrhnl
AY1
ffts;:i,*'H:ifiT'ffiJ- !z I ^'#
cire equol , so l'* c*q
'trr'ongig,
-Vi hrrn c.n i ..-.L.a,-.t:
lr*J* ".r,ot
&-= 4-?, is, .^.*grtq
,''l i
3.t: i
lt
te8io^
Co,rlettan c,oordincrhe- sL1sbe,rn.. fo ofecs"FLe: dr ireootre vccfol lt].i1p
sL1sbe,rn.. fe9f0fS:
e Quaolraxrts l{a ,!Ompn9f : ve"}or Ax
$ | ro' - -F= A', 'Rl jP-1.*'" x-.*,p".",t vec}or
=
l ot- thc x1-
x1- lII -1, ^ lt-i.o'.., "{i Riotonl xrqxis
I -/i "t R otonl x-qxis
R'o,j {t ferrndrc+ata("n ,o*r, othe-
tr lO lolone l)Llt, jcrmponent
Veckov It = I r""toa
LPr.i..t-hr^ o$ t
LPrq".rnU-n oG
R.YTtr:nXlre
corrrgonens, og.r, yu**tt
. O lnr of it'e x-cornponenr ftr =
,J' I
,tP" ilh&
Aldon5 !-cf,Yr<
Rf'.r,
"$ ^t^*' laxfs 1
fncranituit c,F {*,e comoonent v..}o" IY
_ fhoqnitude o$ the component ve.for AY
OfliQ- 6i$n cF AF=LD A),r poinrs in it
ahe pcrli've x-clirechbn rt*) i$ Al prntsrt-)du. n.A'
{0 t ^componect Rt, a*ornrned e..*e rrna.1
iql- u"inq );.,i-i;uhil unXii'I i

21. --l5x -
t
(..
I
-1-
I
it j(-)
I
L-)j
I
I
i
-t
I
-1
I

22. i
__l-
I
I
= F'r
--.-., I -- -.---
w o
x:
-1 1'ltcr
I I
i-.'-j- -!--
;li
in+-[-
r"f
ii-
I
I
il
I
.'-.t-'"-
I
bur , o$ inA
i-- '-"--1 .-'-- i---
Por erht l
nt o$*-
I
I "t"
r-l'----
l
'

23. 7l
- D..rtn3 the-: ocr-ecrcrhpn phose, !. 6cfe-r
vterhcor, ckc,nce- oF t-lorn. A/hc,,,Y's the-
, AaXt"rre c*f Hnq .{tcl o0 i lrhis rtrrr?
fr,r.rr tc^-kq? :o,rl?Z
l?orn .6r
I l
0xe
EfnO = {rsorn :
(Vil.=c)
O= 28-
O,r = t16in9
l
rkrurun, ga6- leml+. i
)|'=Orn ,'360m-
,
= (9.6.1")(si,r 2t)
X9 rfr.orn
AI' l?orn C)* =
)i
ttl.U -ls'
16;;=onls
ki =Os
rcooaer
- iRolter cooster ,fos ars +o!. go d3crrn o-
oq&d' q 2d hill wl a.6lot€ of 36'.
bcftom I i,,f lalr+6 lllarn z,eis b ot'ing
f d*re.m"s s€. iar mq-les
vectanF r-s
up,1+r hitlr& 1
oPtot{tt€.'' 5 *
o[ Yetxt 'r' /-
d-230'
* I w.ril va-..v.
, --e.. "+w :
and haiht crr$F ts crccr)erc.}ran fhe grec^fes+?
s,-i" .=?i'ft"t oPP= H,e{ht, AD5' U*u*
I wovd tTro*3 ,)
6ose
sin-' (*'#Ya".se-) =r 0
_ LrPeePesf stopty'
:
Grrecrtesf acc-elererfibn =Greoielt vcilue o9 'e ( /,,
h errq (Vr).r^ = 5*ls , (vr).--- -(V*)ac
:
Velocifi' ot.$grlos ys,'-sive
Ann^1 rc)okive- Lu Carlos(vr)ac-- -l5mls , I
C4-;r cora1p,ir1l
(v,)e.=Lv,)nnrtvrJo i r i i i i i , i i i
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 .
i:'l ,t :l ii.,

24. 7
I R.-T
6.xr 3.qr l{pr,.} frkrl ts o. sgeecling buef?. . I . ,1
robber. dhile drlving e.f 6o'k , t{re1 fi're' a ballef
- PaLt.e. a.re. ch.crsing a. barrt<
b gno""l 9Ol- cr- h're oF h;s <-o-r. l'trra gaic-e- grn s,hogts 'b,rets '"r.tt 3Potrt
Nharl he 'bue-YE sp.c.A re-crHve 1o q- Tv ccroercr cx-e-A Slzrn4;,.a
tD +{^e- .rc,o.<?
ne-x{r (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* v 1> vehicle 'llrr"o'es fr'Er'f,reldfr'v
tvr)ac Vof Bullel retahw 1o b-r =so,sr, iutru= 36o*ls ;o6'fittglo"ffir!|Affi
ftnd 1vt)rer Bulle| rctahve lz 6rou'*,) ,
- Clevelatcl rS etTpro, 3Al rur'leS errsh a{ Chr'cogo. A pktne eaves Chicc^jo t1tn1
dU e eoS{_ c*y &cs,-.FL,. lhe 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- po.rrels
,
V3toeiq febhue to the- Xrounc) ? o= ta.n-t (ffi,)
g"" a.(r
V_y= pla,rne fetcr.ive b crir "-Sooaaph f m {t v,npr,) oJ*-r= 9: lt"
il^6=-a rro Crr.,.-rncl:loorng
fft-= 6to rnph
Ve
chrc-(rfo ele.od O VelaiilI 4 pt*e
' relo$ve lo the qrand =
fqs f,tS : La ro mgb, ll0 so,^jrh e.s*) x
"1,
6xr Eallg Slqin 3 thru ttre cuir, tong j,tmPers, ,ct4cS doing 6tunt l"TFs
nh obJnil ftvxl mor€S in Z- Dim€rrsiorrs vrc)er [4e, in?luutce Er
on [y C=r rarz f ald nctthing eqe
.$1 ,neglec-*-"g err'r Fra<.iRJa.rrc:e ,-. rrr ?-jTl'le will foow |he Same pd-,
fngarleC-|1hq *r resis*crncre/ cr-r11 gtr,
g tr?tec}?nS r.r:l the- rYratherncdr'cca 6t^rrr o€ a F:rrabdcL,
dsr.*tc.tr ' L9.to sle', shcr.iXhh d"wr) Cf,x=Omls' , dyE -g= {.tOmlsz
crcc.eje-rcrHon iS cr,r..:ar4S +he- scdr€- sI- q), goints :
*(v'I ono [vr)i Y t .],
- Z/ :F veoc-i
Y Vg'rh'ccu coryr?oTlf,',,s tu*1 aei.'rxl
ce.crec,se-s l"t , 9.8
not cltdcu1 (b) {F |
r,il"i -'
Proiec.nle
-r
lqJruh"d
cn onqe.
hffiT., 5+t
lurieorp,l hos
o
u
'
r
# i-ffi
E I /',
l/c I -
I
],, iT
-0.r.
T; #H-##
{ r- *Bcutt finrEhe-s irs rnoh
t-) ode{Ur); ry" (Vr)i=-Lvi)+
Ipglng-:triil,qilA4"
O lgrrr'4h
t
ba.ll throhJ &wnwrd Analg
f-am rru9 A a ly,il)}rn)
U
l,;1ei.oirs, .n:ffiri3tl$* v'
',./;
to0 hom horizonk'r) lhrouqtrar;t morion
erf Oe"ad u; *f.i^pa'
Elvo*ars of rnohbr, fit ltre gorebolic kctlectorl of a grojectiler
. Xf --X; t(Vr);At ' (V^)6 =[V*); =Con$kr{,!l '
' ttVr);At tVr)q =Con$krj.,!l * I*oriutti) , v<x
kor;ut'r1zl 'Verh^ote corngxrtyr
,h=; r (vr)iAt -*qtnt)' .tv.t)t.," (v1); -tat og proierlile rnohbn=lnadpnder
ctrraviq
t I tri.ihe loloors cr- parcrbla hr"ier*0,1 l A"l;+*'S "Jlo
f!' ji'31*"*.1,*Te tg*t belor^r o- ffinc*^r
Strar$rt-ire. haiectorl
" lK-
rrc1tdrur1

25. 7
Ei6.tl -6ugflose cl. atunt rnan driveS c crrr pf$ o, lO-,rn-h;qV, eiFF crt- a
spe,ed '# 2o'ls. [h',^r ft'r does the cor, lcr{d from tte' bcxe o$ -lrr.vlllci${
l
llurlr, lrr^. re- t,Y ] ..rardr'J llt)lrl
,, ,l!t:- v.^U-L rl the
"y-
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
o
Qx= 0tlS"
&1: -Xr-l.ottsa
Ex'3.L- Cvrarccrers hu* tV.*dAre on <x bt ttr-^r wirt <xgocle iG rts eyeerl
cjrops bebw 5Onph. PrOblem: A e# aer-hbn ol c. fr"r**l overpcrss is miserrq,
thrr1 dec;de.t imp ttre brsover +he $f. (oc'ct leadkrl up to breeil< c..s <^n X"t,
oQ 5o. BrstthT.neJrnq 67rnyh .^:lren "ii htts ilo gil, s ths reo,sc/gossibte?
J ' ' jf
-b!erv!- 6'na .
;,---'.o* t- _1. u--rg'n ,l
[Vr); =, g =;' 'tvr)i o.' ;l*f
co$e^;u,
)^''=Qo.h)*s(a) 0= one.c"Jts{st):{nt'f;fi
t,=os -l
."gl_ ___j =io-fi " o=Art(vr); -rz"1ar)
r, =&'/s ISL#,b-:L"
|tl.-.1Eo./s$|'l-A(');=Vi.:irrt6)/79=tvr}.!goJil
.!.j;- blrngh
[Vr),
$;]; l't;:,:)f';-==t#-
0=6f -il/6ffi
l ao-b
At=()bs;
o =At (tu11; - !XAt)" hqs- z
tegitimcrre s6uHons' 0 ha =os <brrespondfnil to
=o cr! bT,liil:qrhifec-rtrg. tlicrnt- to fin"l when 1=0 c,f erd :t-k$ ', ,
uae'. ) L1)i-
urae'. 0 = tU1)i - ZSAI
1-qAt Wr); =;S)r
V.,,1.. = -fu.,)"
-
To cYrecK ${rsrrer tr,e .ltrr..i fo.e-oF ond ondinq are-@ acrf,ne hetqht, tot#+$p
Nr)+ = (vr); -$ at tvl)+ =[z.b*ts) -Cl.r^t*)b,63s) Lvl")*'= -Z.(o'ls ,/'
-A
Foolt?c,.,tl-Pi-@kid<s tte 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$ejd ql. ttre sc^n
(vy)1=
Vittrra
re=
ryt s9e,e<l,u.ttrc-t5 +he max distrrniA hecpukl of kick
0 =to'[stt*3hh-"P) How dirhnce= vf
lr)i=V; co;ce !*i '?:::'f
Ronse
" ilTlii";"{l"g#=tS" l
-- [zq.sTt*tl
l.?-ltt
x
:1
:
*he
'
the ciOkrruce |
Ronqe : fhe cdOkrruce lo *he 3 i= 23{.5"nls
=,bl; rn
l+--o
lcndtnl por'n} a,lr ralhrth ls=
lcn{tnq poir* orr L* 0
h"0;Xu*SLtN* rr,,ni1e
=
u ctskrnce-* O:15' .
LrHo,,, Cista+.e
i..1 .2'1,i5'
t,
ISHT;Y::)$=1s
xmo.x =tvi7$) .*r /:
hr {6' o*r.)^ :

26. 7 I ;
:::_ ' : I , i. .
" PGr'l
;: ri lliill #'; '
.],ii-lr rtiliii
-Uniftrrn Circralqr s-gseds b,rhi crfnti**rsl ChCnoing
jttrill'
dire.iion
lfj,,,il,li -l
'': ! - i:l :
I;n e lnlqvc,l il lufes tu qo c^round:cr circle ,1 |ime
- r'
WnglehnX 1 reol.rh'on (E) iI
i
iii
T= r tt,*je-.u,"jj' I
6x'. 3.9
-An crudio CD <pios eb + ug to-,5!Loi.V*.,
$cequexre.1 .$ A! 6'{o rjemr how rnvorfirn<
tslequiredbronergvolufion:oF!eoo3 ,j
fequired lor one rgvolufion :oF !g=, cDl - ,r .ii *i ,---,.,*_. ..r-',
*i,o- ,
1.-- 9 ' T-.t'os-t l=o'lts
r $lg-?;m ^ (9o sacoods
y = tsrr rerouhors*}1ti1li.B. = 9.o $ =t.os-t
i i i . , 1 ,
t't " ,; ' 1
s Z'rrr
Zni n
^fi"qe rne<,.q;red .ctoct**ite ?1 = lf
O*.r., =
:
Frori Lt) x-qxf5 hcrt L-) vcrrpe
- --' --'-l- = I i
; 'P'e-Y ot".e i i i
t = 36O-= Zrt- rcrcl
p6c;
a
erns i'&;'J;]slil"t'HJ*
Vtr._rv.vvswr Sr it A
*,.ia,= t,r*r*# = ,
,
d'' *boi L+l X-crxrS ,
":" L rcrcl := BJ. b. ,
' i -
S r : i
.x eLpaie'ns)=? : :
q{-llglsrb
. -a ) -
u>o.ngr,rloronits I .
r , ;. :
i i ; i
i .
-EHH[^-{$TL*d; "'-J"ill
lc"r Hohon
Le-rrhctgetal frqc€ler-cl'tioh'.
d ;if$n
Accele_rcrhlorr
pofrrr
**rs pofrrE
L>congtcinF
the veloofu ? .at.*q{r c-enlct-A[,,.E$L A?
twd'ttie h..c Llrp Srrrn,
is alurorlS ot |he crcte filnlherEc^r.ne
Yrcrs
I
i" $nci
Tetfxt to lfre rndl'ron dfcrqrc
rnoli-on clfogfcrn
Cirole and i)
P€.rPendra;br
io a of ql
points'
i r 'fisfhe
t
{
?-l;
o$*.l'#:ffi Vecfbr ooicttshwd the
c.enrch oS tte-clrc)e-,

28. '.j- -i"--
--ii*--
lt
i _L_
ll
-l- -
_L __, t
-',-A
li
--t----1---
-1-
tl-
iI
-l- j
it
-
-i--t-
i
-
|-- 1
- t-L
tl

29. rlli
lrii
ii
: ftt?c-ft.tt
:lle. s
fl.o.i<.Fi,e
. r&
OW=teta- (W) : 13.J I
-lhe erovitrrhonol pull o$ ltre ec,tlh ori Gn objer-l Il J,C
If-l
l
u
- onq onfl- vtrnqe to.<-e ' ' Bcr'll aD i.-r I r g-$ *t
;a
*"I1$b:HsilToto. a, w11s i nts
so
"#3ri5JE''#
i'H
t(NoT-lhesGrrr-e-kht,ngosmcrss* , , i l r I I i i l
,-2'iti,i,',i 'iti
/=
#:'-t-l l-sp./ , , i
l r I j : ; r , i
rl
1i',i li i i
ii I
- &.,{s qbrces
bcrsic Cpntt.^C-F Sbrces
bcrstc c-ontt-rc}
IPush(rih*,c-o.npressed) ori pu(Wn"shelched)I 1 i , .
-
fftrfflt:A trffi
i
, 4 sheto!.ed 6pri,B.x:.5 _1.p*tt
ry,.*-
$orce
f
@o."*,.,-*=,-
:r
6@ci)
<r
i j,i contl{
oi9ch, exert
]l
- When a roge or wile- p*lls
strfng gn o4 Srcc
- Dtre-r'on g,S-Hn<- 9<nSdon &r."e iS iqtqo+fS rn Fhe. cl(cec-h'on oG
'*he ehrin3 or ropQ.
Atomdc rnocle-l : fiD urrler-E!^nol lhe behoyrs r ,pr,qper,treS o0 F{e{.ros.cFc-
"bj?"JF
rope ma-ce oS of-omS 3oine<l {oge*her q rooterdtc{ boncLS-a it<e. ho5 syr'S
ptr'n3 on the, errcls oF a or roPe skre-tc-heg t''lne- molecrflcrr eprrnns
"h"3
feltsion ,l'iin +t* rope ct-r'rd ferrgicrir"r e:rPerc"ttl=.rt -
.
Lu""to srg6 -? ,
obyc-t- ..r fti" dtl oF *e r-oge t*5. lhe ne-} sgring iG"r-e. berng -'*.rUeot ,
bi billionsrbillio,salf picroscog,c6err:np[, ; , i . .
l; i , ;
irll
ONlornr".l hrce (il)
i;i;
-Mvrwr./:ili :
,li il
- 6r.e- e.xe-rtecl b5 cr aurRr<-e- tthe. e.rtu,t) agcr.in8t on ob3ec# tlncrlr is
pressflg crgoins+ *t e s.sfuc€
- Direc-trin L perper*icuqri- lno S.rg *.^-e$q. (l'-) , .
-Ilne sur{r^c-e-" g.rshes oosu
the compresseo moecr.rlo,r Vn' o.3crinsr tshe 'bo*'orn oF
Sfrio$S ih ffto wol lcreES {r..-- A {{r
ult*t,,.a aqurnst-t.. vr^nt
_*Jil:.r!,o. ts J-
{; ke' *,e
f
+- L' i

30. ll *j-i--
i
t-_
I
I
il I
f'*
I
tl
it
-f-.1--"-
l
"i*..
ii
I
i
r-l--
ii
I
*r'--"
i
*r"*
--i
I
-i-*l-'
I
I
i--l-
ll
-i-*-r-
!i
--l--r---
L-1._
ll
ll-
il
ii
._t,_,.,!--_l
lii
fr
Iti
^")l
ll
ili
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l-i--,-
iti
itl-
f - -]-*--t-'-

31. :,r,i:iii:i
il,riiii,:lilli
r i 1 , , . : ) i ', : Pcaiqi
I1 i;lIri.l, ii',
.t.t
:t, lli,r
i
.: ,,
q,slVrlhcttto, Erc€sPe? , i ;i .],i :
iili
I
illl
-An oui.cr puN.d,w,iH^ e^ c.onstorr" f"t& *.t;.tiwi,ffr,o
-,fhel'nc*=-i..]r-.t'g)n (s dire.c,t1 :9"ogo.ftonq,- 1". +tte 6f?e oF.tt+ C',I1E.F-
-,,rrrl-,]'til,l
li
'c,astont,0ryt",fl'-
,l
- Acc-e-erchbn s nve-rse,3 grogortrbrcrl to the fiurnber of btocXS
hcrelerc^*r'on7 d irecttl
to tte
Inver5q)g, ' A a..e-
-'= T .
tt',ro.tl
$ bcrrrds a i Boc.K n(co'neno
.- iC{=o,r 1(r Bbcrs)=ffi.r.p'4
,ot = B.:.,
2- bc-rids
?$i
a1;a
2 Boarg, - l$ ra is in*eroelta
i 61 =tcll Proporh't(g.l to x,+heF
t b"^nc i
O=Cr
VgOcetr,(-V y6r..6- r'me C;rY€^ph
Btocrk gutlecl ta1 L,L,+nA 3
rubtoe,.- bc^r.rclS
ii
i
Mcrts :
*,' "lnertrlep', Ts.rnaenlr.t o$i on objec}:h>
-Acceterqbn iS lnverse1 Progorhirnerl
:Hcresi= +he proge.r o} q
Accelevcr.tes i n r€Eloonsg
rili
- hhen c,. rubber bc^n<> 6tr-e-+-ced tr5 gv , <an cr
iS clnstlr-nf Sr<
-!he crcce.erc.h'cnr o{ lhe lolcrct< tS 6ec^sucec) +- cr. b!o"J< piV
hi
,Cfn Untcnofn {)1&-bS fs gurfrecJ url {.lne- €clme robbex Sq-rie brc-e-r:
i s ctct*-lerc-l$ron ts S,Ohls3. Whcrbi ++re, mcr$s bf.rqJ< ?
irr ,
fit= <.q x O,r ftlsz
-:t
C^ 5.c>i'1"'
E
ocre)eruh'on=ffi _E- Direc-hcll og ltieqcs.ler.h,I
Q= i. ffi- ' rF r'!re, sc^Iae-i cr$ tVre
*' .i .-dtreeitrn oF +h- q-..e.
r
An objecllo{, rhcra6 trn) aubjec-t.c! tr'
Wi Urplevqo cr.n qcLelerc*fr'on d
't.Jr-.?
:>
(-)= m
F""r ll
where- is ;tin€ yedhor
aurn oS tarce$ 9-h,l
ou.r-t ue$ord,]
iil
pnl
itvr Vhe 6c{rne dirir}r'on cr-i i:
R* = fi]'d (s"rne- o', ' ri

32. j
7: l
2.{6,l
i
- Reprcaerhbs +he, .Fje'+ ic"s, cri ?r.+'c-e- I
;€horx$
l' tu.- .,f the
ocf n3 en the- 4-;+. i i i i
lr
i,ettl , I
ltjri
li
i
rl
Ql oralclrt{
'll i1
ri
ii
ti
ii
Ltre^rotor .iS crcre.lenoh'cxq
t
li
I fn.t ri
tt
i::1
r , . , | '
ti
ft;,9rY' :i
r
I
'1
r-
f)
B"Utor.,1
rt
Sln4pSicr SrnrJf, rnpetet rc-f<e.f, b g. bt".fi( oS , tcg. .a"4 I
I
I
6h6crk i| erross *{n. smc,e>rln aurftrc-e. of e. 0rc2.r, .[q-l€,.
i
l
I'.
i Ft'chon ts nel,lrglbte--, Dro.w rco. l,:puc*t cr,vervicl,w,- moh:.oyr I
:
Ctogro-r., y to..q. fdenhiG'cc+r:on cltoq,rc-sn, <trrc} €tee--1U*
nar'md;t€dlfF

33. -, -r i6phl
' i t-zi

34. l-u-
| -? t->
fqh"fa
-i-'_
t-i
ii[-
-L*-j--r-
I
r*r-*-l-.
i I
-.ri!*-r Ph..'
I
----J---
l-j
i-i
-jI
i

35. 7
Tizrrnino, tPeecl (Vo"'*) r;r irt ri
ff
L?Spc.-cl :aF.llrtc.ln Hne
_e.ra.r* bc^.fqnc.e.,bro the- up.^:cryrc 4"1t S".ig Grfl
+lne- downnrc^r,C we^tht fur.*t ccrLBea c.1 objec-l b $<-] w<.r olituSc'No"l
-)Onc4 6,g1 obec-t hcls qecrcln Vte.rtrt, 'tlr wt con*nv€ fc^,rinq -*
- "o - l
lhatspeeet t-vtlr &hitslheg**-A, . ' . l ]
@ a , Iy.*q' x A heevr'er objer-l.hos'o lorger l-errnfrrcr.l tgeed-+{rarr
Vrerrn ='.1 i;{* R a. lrghter oUte+t -g+ ?q* Efee x
o)A* low gpe-eds D
lA* |ow speeds (to-ridr'crfnefer q,p dl rlross=""a1lt"s Vternn elgn(
(to-ti-d,'crrnetbr ep ,ol ryross:eo1 hc.s Vterno *lgh{s
,'r, fti
rZ, ffi
r's srt+t e^srct +he Whie l0crn-dr'crrvrerer lerdbott w:lrt*r.=6 q hcrt Vrer-'l€oql
,
r/
la7f _
bc.$ f-otlt ,-rl q =S U J iP Ex 5.3., Terrntcrc.l epeeds a$ c^ skq$tver arncl ec Hcr,lt
b) ns v rncrecrs< sa . >
,--i,g3f *Zos v+*'wr=lrl@
.
c{e-s D. Thene-} 6rvc. l" lr"Y-, ,{-1>--t"3 :
anct henc,e- o s*t srr,*tter + t %S e-i- -i.r , # ., = [ffi'.u
',l
i
irr,
r ', '1 :etni
Vrcrn J -ls
c)6r"",tt*.ttX, V recrctre c vcilue t.t>r , l
l"r=S) '
the bqlr falh crt aconttuf J ;S
q h;
Srxh'ltct D =W. ttev, 6.; =6 .1, -:.f frt Vt*r. = .'1 (.21 7-" )kr,iz,F)
srxh'ltct =w. tt'evr Rel- =o i
ond " trn"+=E V.-r...= SG hls
6pe€d
tt Sc'.me rOeqS c'-tp.1 to oecle movinX horieontcr..[.1. creett, bh*l^. of Shot,
honaontt-l*S, S caDscs ab)ec-lr b sow cfow . Terrnir,c.t sgead Whe-n D = F+n.rr$
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.toe fo grogo ie,lt ciutcf *r,.^,
$l-e{ ir6(nX tbtr ciL.,
Trlptccr- pcrcrrnecivrrn hc.t dr'cr.rnefer oF 5A*trtl. Whcct's Hn<" clrol S'o.-e- .rn ti sr*iirnrrr
c.. or spo-d oS o,es-^lsl lg its rh4ss ts 1.ox1cir <3, eskrneli ha^, lor.rq t bcAres
Lr if !o covne !o a s&op r,nce- tk 5;b96 €trfi'y6ryriq. -) Etcr_€
otlce it stof6 Eu)trrrmrlrc( C;t=H= itY.l
,rc.e ft atoeo ,
> rro-ldl) J
-'2-x(o-rdN'
-r
D = 6rr (o,o9^r s'l/''.zbxrdqtn)(o.zsx rg't ""t-s) c=^-ffi6T8 1.,1211."i .usf:lt:
AV - Av _€_._2.5^to -1:-
-.rlzs .
D =t.Z*lo-'oN O=5E = fr At
-t2-mf6a A,
" Port^rtr..ivvn covret to cr . t = zxro-ss = 2cr;.rs
f , -_
v-- -{-$ <"nnr
F.roo.lsion
'&'ffi'tTi'S,.HJti{:q
ho.r.rv qlrnos! inskrrrloneoosll ,c
,.,tffi:i ;g;tT;3
ftotvnni5
ctrirecHl aroFortr'snrJ . ] ' t"Ju,n** o*"ee it starts
;!t te- prSgrrtton [.s..q
;_ , i i l';jJH'silI^5"GJ;-'= r
,
D is equo" ond opgostle Fsropust'on

36. ttt --'f-
- f- -1
I Fcll l
:t_I I
-lr-l
t-1-l
i

37. 7t
.t)
Arod 6reb+d
5
ffi
Hon 551
tScr&^se-
rhg.bs oF lE6o
o-ts cl 20'aalge-.
l-en.,lo.l tn, the
I
, Thei
I ''1hq
l'

38. -A fic€-Lc,b
hortt.tnt-ft3
aruX Srce scls
, ,* thnts|
. l-
Prtoh13
1rr-wn
Wo Sebsr
6-zzoo
F*."ei i ,-ocpr),
D = !OO-t*t iF-,+
, Fnel
rli
::i
-A cr.r1l wiHnt c^r mc*ss oF hfriCn
[o:n d 6zoU opp.6"s l.he SoeA
trorn reEt tD lZh4b in 2F*= {* nT.asOF rn'g1x ii
ii
i
jri
T.-;g.-f*;IYl'Qy . :
I f.1-, i
a- =ff =1 t.zt4"'
:
1r
lii
1:
l;i
,)(."owi ili
-.. [V$'o'lt Tlq5o(zeJ=i
l'lt") r 3?+N iii
il
. At = lo5
(V,*,'tzns ft lr
iti
i
lftSzou ill
iil
,
rli
rn=t5tokq
'
ili
ill
0 =20' i.r
ll
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l
SP tl n3 qcr*les nneq,sore WeiEI.t, noh
c
rsp
+ Spnnq-?u$heS uF
(
r..5, . '.5t Bp-r:
I
i
trlre;r =O i,vg-werd 6pnng
-
.
rnutst e-xerel-{i{'bcr$ge the
downwcrrd weiXhtft>rce. :
FsP" W=g '3
lil

39. When d--A , F',<'r= 6
: rnovrnq Ooi^ru, Wl cl (-): veo.i rt: ll: :
;;
reqnttesne.b
Wet$htetsness i ;
'.'illii ,
. -n'"-"hec! thlt r's v{etStless hos no Agg.rent wetXht (W"1e1=q)
wetXh$w"r"i=o,) ,
,
i,
J: ', ' "
:ItT'
Perrorr's u1=tY!-fl
J
3ril ,
-'_r *J -'--' --J.: ) ftrll qull. Hne ;6c".rng cl<+-e,f-elce$r
: -* Weqht Clt' -nq
'
| rltl T"
l_^.1
,
.^: : rerncring true. ' .1:-::j"::,Si;-ng e,$$9,r+ -l- frcr.e.lersrhon (
l=--x' 3* .,$$g.+ c*n i'-- --:- -f-- (or
crcre.f€r:srh'on
:
i"l**-.T'=o
, ,
I,ijiiii.i,j,iIri
iiii',j
,:l'li
i .::il
: i :
l:iil',
I
t...-
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- ncljstq ilse$ eo tslnc'b t{"e.' oblec* lstuqs h.
!utl*, +t
Surftrre=wlt>genehohi|. ,o^. I
.,liri ; i i , I I
-' . i
:
6 S3: ruorrncrt r'
E -a... . ,
i15,1: Norrncu [n"q.e-gn a pre88ecl bolK
ror(€- 0n 4 p**.cl bodY<
r
i | i
: ,.. t1
' ,l t ?- ka h^.rla li.s., on.
. riesl ^^ 5. -p nl-Lo l-^.{V r's ^A R{--l xQ.
?1.* .,:rrlll'ilili
Hne. norrntrl fuf.ei crdn'i.X; .n t"h- fi.l+o
N,cr.
lib
li
Z
w=F
wu
Fy;= h.1
" WJ t trl = f -iW1F=A
{1..i*X1,8'f") <tlrtlDLN
n :-i!aN-I
BrJ-i-
_ l_
f}:iY!rE--i.-. -, f-,-
;t5r$ *l*- ,-
i t-
itr.
I l:l:
l--l
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i.
iir
i--- -
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i l,li
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40. 7 ti
i
ii
l
' Fcrytes on 4-t^ objsc-l'-
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