ll,c1(e - department of physicsfiete/hw_3_sol.pdf · knle&r"ncn1 af* qt"gng ll,c1(e...

16
@ knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE- ?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot ) A fr = -rt L# {-T ;:ffiP''n qr^r' o^ o. <,J16 J i L*.n--J t--- l-J ou"ft"o.*; tf; I Ttnee\e^shla "{ & =v +tiil4, o(r4 dc{^^pdho' ranr,orehl.o, .(ah lilrt, !l&t *at t n(lst r er6e','iolr= -* f' q,e{- cl'Iqea}.eni-c*"d-q +* ffe&prJ 4*"lg-"za,rpU &ff; *fs sil€*. $oleg *\*h +h€ sand€--*nurrrrua *id"'r*r5 ,orc*epdeo{ 3p}hu*4oo oqs slils tdgt^heyncob &r'Lh +w {ndn! paseluv ubv-\ \ ,.ha,l, w ,,tr &rMu"{c tb topul.*h *t 4+t rp^, ry ,nLLw7o7,,rlol\q 4Lrpi do,ra €Jly}'^ns over lte 6iv*r W"e-g\ler>. Le+ u,s (,v*^weu,t o[ -hose drYynL*e, ds 4r0t6,--. J.e, .9trY,erv,4*""t" wSx,hM I lao2o = &('l 1^b^;"t= u4 f rto/a / qg $wo"d *Yrl wlwre &= #".1 Joubh '*:r,I;^ffJ;i A+ h*l& frH"O ( ;"4.J e ?."^sila.r,r ou",ag) , ue2ve no&*bt;ocald bk+ giles , rJTli rnp-&ubly occupi 'd Lxnq-gikGS (sw,nd sau{iN; foa)e) '- ikOo a^en4zn*,alc6"n,,d t3l ub"re N =Nr+N* +"1-+ e.A2h"$* @+l,ejsd*-Q, : ll ri y(w'tn +hJ 6.r+ orJ", pJtrU*l:^ l^ a, sec,r-l-o. A^, *! 1-t*- lr.rn -rU luA' 1n 44'e sol"n+",n

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Page 1: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

@knle&r"ncn1 Af* Qt"Gng Ll,c1(e

W-n*orLtE-

?wbfui"r Llre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

Afr = -rt L# {-T ;:ffiP''n qr^r' o^

o.<,J16 J i

L*.n--J t--- l-J

ou"ft"o.*; tf;

I

Ttne e\e^shla "{ & =v +tiil4, o(r4 dc{^^pdho' ranr,orehl.o, .(ah

lilrt, !l&t *at t n(lst

rer6e','iolr= -* f' q,e{- cl'Iqea}.eni-c*"d-q +* ffe&prJ 4*"lg-"za,rpU &ff;*fs sil€*. $oleg *\*h +h€ sand€--*nurrrrua *id"'r*r5 ,orc*epdeo{ 3p}hu*4oooqs slils tdgt^h eyncob &r'L h +w {ndn! paseluv ubv-\ \ ,.ha,l, w ,,tr)&rMu"{c tb topul.*h *t 4+t rp^, ry ,nLLw7o7,,rlol\q 4Lrpi do,ra€Jly}'^ns over lte 6iv*r W"e-g\ler>. Le+ u,s (,v*^weu,t o[ -hose drYynL*e,ds 4r0t6,--. J.e, .9trY,erv,4*""t" wSx,hM

I lao2o = &('l 1^b^;"t= u4 f rto/a / qg $wo"d *Yrl

wlwre &= #".1 Joubh '*:r,I;^ffJ;iA+ h*l& frH"O ( ;"4.J e ?."^sila.r,r ou",ag) , ue2ve no&*bt;ocald

bk+ giles , rJTli rnp-&ubly occupi 'd Lxnq-gik GS (sw,nd sau{iN;foa)e) '-

ikOo a^en4zn*,alc6"n,,d t3l

ub"re N =Nr+N* +"1-+ e.A2h"$* @+l,ejsd*-Q,

: ll ri y(w'tn +hJ 6.r+ orJ", pJtrU*l:^ l^a, sec,r-l-o. A^, *! 1-t*- lr.rn

-rU luA' 1n 44'e sol"n+",n

Page 2: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

Ltd(oo/ | f'r loo>t"t uP g,*r] = o

@

{1"! i, a,rot!-s'uurt ttt u!,1. eI qt^""t*a*ec,h,l'c|tdJ

Eqf44,. phich h,rsNo*, if p

gN so/,tt4ins Er[) Q,nr* u, p,Js u( 2N voEres /rre.lu lngwfi,

"^.\/g te.on -1V",+ 1( *e"s o *toHx n-b^^l 4 +t-l-'rr-

' &) <ad lftl o^)o) ) ane daubts oc^vvlm^* ^4

^" 11"; ;, nmt -7era onla +* d ={ because- o?er*., ++rffire4, oneQprJ-

trpe"6 {-.'m%,i,Ut, "ol,pi d !-^+hq- *kiWii;ffi,Wrffii}Uhcrdle i (+l^*f beutr"s "Lo"bl,u ,ccuTid x#er*or.d.s) , i,4,(ot<&t{ +t li"Jt+ o o,te fu, },.-t fsJ.

,As o regril+ 4 +b. al>,ve ,Ihe- ̂ tn'x de^e"k aVVear\n1 ,i an.&Idre oll ze- (sr\rcc b0 {*toras we've e+g -*lnn (ur+h;, -pd'-}*+

."t!/- 4llsi- *Jr" enerfly otrredi,r,'rs Erg votnlgh ; f .€, 44,,e- "leg**%"o^oiry: .^.a p\e{e\j w"A,xrep.J.

.,Se*"J-gr"lu f tlufu,litlur *l<"lntt: We) il ogo'n ,rtottq vnau,{t reau!}

.4"rn se*nrtA a+der prfurlr"h n +\npAA,^,,,o,-f^^y

-?srr'rr o,er $vnun*t Lr[ diubA-or*id la]'l)e'sik')

L [^ ] ZZ "'(oJ lril,r>p) r"r("roltln loo)t'r tr,€'tr"n,] = o Wi la+o i J

,Jr over GS lr**O 4,6,6..,

, Lelns fbU *lh'l"he Atub&l_--ofnx e!s-,"J 4errn a fi+-lt*biL:

EI") - A')*r,t$f-

ofllra "l

=llein 6n,r1r;

_bu{oa

El"- E!'l= u>od*" dr r @) r( , )

E o - b l

i"+ ('<rr tfi loot)t'))* c')(d6 lfr looT c')

= z_z ot<o/. f ffi I oh-)r") ht <Aolfi to+t t

= -'lu h+ to)4ocx/ {f, f d a)(ot d <Aof fi lorc>c"} ^,

Page 3: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

@ II

, .i ,

--.,. .P-*ble-alj i

'an Tf, \k+ldo)t'l .!dcar) fiholo -

I

i ..-- ..--,' ' '- ----,_-,...'...1i

Iyff"otos,- Lal- &H,ung):-

--gsl-,

ts,#rir /ooh" ve^4 m*L l;u-1fuetge^,al* q*4i.'r + dwFLL&- -- -l*=cf\re-goqnl4+or- U" A'W. ,zhjah U-a"fur*t q

: r ! t

0

1'c*"*" - A = p^jbrhrn- tp",alw,Mk *he. < u brf c+,,,[tLA=-o -@AVg

- - 1,. -[leL{ u,e-ret*-ri+. .u" QIuA,re- M^ d}},nir^ - h-Iernt-fnVrL ryh"s'

- ,.-_----+.i , r , I |i n , r r I t A - r | .l:Bea^rse ol *,+op*unq. o* owzalrrrP, , +he ̂ -b,iuhoq drdqaa{a dna' -- v |

- - v [ - - - - ' - - - - -

t

Page 4: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

ffi'w ' ' - - " 1- t l

I t t Iv

l

al-//e"-d (d=")

+ . .+ .\,0U \a),qa -t

e$

t-A

4j)rd1tt 2

"lrn

<6)'a4i),r

At t

{, =!2 c,cl

Page 5: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

@

-_0^hlpm l_ - Tm-vr\6fct,

)Jv,L.,b!4k

Page 6: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

@

- 6 (* ^,*iA =? 6. *l* n,e'll ,,,,aAA 41,'-,#b

A ^4 ^ , v t rn r'6t = ra;t +tiir = r (flr sgn-tfzQ,"';on$ . Qnrrtsrrber, t A , A \ t , X \

' A . ' I=

5 (/[r -6-ninl = ! tta'-f) = n*-tfz qnel

nitA3j*

= tr -Ilz,Tv.r*Sre,' rl n

f,(+,,nlottf" =t,l+ffi= il (*(rnht,-mi -"S*r) d'

l= u+*fc.')(&4=p;4= d

lA (rs;sj' + )E+\-A -){/

=il;(asi.s3z + *1] a

i;qf - r

)3.

I)0

, l,J

to

A?o

3l

(fr'i l7

A7:.d

' )A

lfeJ

'J2,3

, :

4

:

\ l- t tt t \

L4,..f

t l

I '

!+l

iS,rbs Hl-l^ e1ns. fi2.t1 - ftz.s,3 h'b %n. TtQ crrdne:ul

=-Mv

-Lt

[1.++ = - s1^ +stytrflA

ililJ

Lr rlr+

# d I+{o , (2sr"s1i+ *q-a(s'lu L.rrL Atil l+{tr P

L'l> 2

il(hio) d **(gd'lsdt A

Page 7: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )
Page 8: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

@F

-gJeegsgsg

- - @:- t/Je-r'rnour'l'ld$$ I tc'-) = tEJIo)- doec--[de)-ra".flo*

=-AP;.;r.d{a-stJ4.JJz.rerrsl,s,

-Ge*4+ rryr) = <1+[u-tfr'* J ri >oq=L<qr1r-rT1t'_J.ilc}<[utqD€(s)-t,6

-=Z- <ry1 e--iffi.-rto c" k;J1 l - { #: i"l*r.t"- r ̂ ;F

: -ard__- :; i:.tffi'*,=L-riol *Lglrr "o{+

,I l l

- { I' -*;w;1* ' r . I l

if;_, -.c-* *rl** l- U-=J"fg+=lil-^.. ".j-meAthLg-'t*s ho *s,rtr I

4 "Tr-t3ro)--F- -toz,4 -W-{€r(+to'k-4o rtd

,*. --L w" ;i"c^i :4v I w!y')2n tl itq{tul

+X-:Ur=

[i#r-a'iattuth+

*;E{:";i'+.G,-f-l o+i&)=19Itol=ft

Page 9: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

o

,rl'wre ftrr *ho Ar"!-y"ae .u,eJve

t(q.,4) = Lr|"

o,nA ac*,A4 lT+La-W-boola',{ i-, PI =

k(ffi)"'fr rrr, Jh"'n tt : +/N- -Thn'.fr,u

fb

Soril'^ (fi,. ru 4.*- y.^*hoy'z fi = *n = FT*Q

<q+l tifi*/x lq;) = kffin'f ,r, /1..- dr*, u?k^-Z*-Wy

=M l*frf h, J1,-, ux?l W.,*(l,u-oq1Neoolent; t / J ' 'L Ph*Lzt^--a

= L,;,,n / ur- lu" I ao,-. . o(fl"- t ex, f qtr t- (1no-q,)1 LLIN-roc\edi t i i

' I L9+t tn=o J. i

_

f-+-

,ci,.o,*g,*rg v*i"bF,l# ;J.€p{'r -fo 3* = .-J-Nrn- qn + IL=o)-..rN c,!2,0rl ir En+,t =

,lH qr* i *.*(n,<- v Pht )

'i,* r -t- - ffiJ l=*, - E*) = W)'t'f=*,

-?t/ ""

= ffi&,, (r.*, -4'ln = (^hntJ-'(t* -z*)" ldqn=fu*'i r t t , t L^

' , YWt

ffi b^r[,,'h an.lt! wetvL

( r I e- ;i'+1q l1') = k ffi)n|

rr, . ., otru -t (W)LN -0

,exp [ilr* Aru-l Ttrrn+r-!".fl =L It+ \"hf/

t*lo J

'=fh H"

Page 10: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

.....'...........-t lI

f in l\ -z l l

&9H4"4--LW"d"c k c*0-utf-k-+1"-ttl+r/- 4 rF.E3 '.," """ "-rf,LruL{' $1,

-&

;[G"4;fJE,*?"1r 1

@ry"ILI'IIIS:Y:

Page 11: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

-4ehtes5t '

{;a;:^"$ti=--r"r)=_

i'r6ffi

l:'<q.4g:$:lt-li

Page 12: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

[".!]"d;NAL - U- t; = *- o =,a I ru= 1+, 1o = 1r- (,m)r(t*_1A,

I m p N \ r z n z l \ r l v t u ' t

Vrnit ruru

ry1snlhfrt#

e*(#) o+-qt)' =

lb

,(-;*N9ooAL*ro

I;,"nN9ao

AL'to

+ffi(u-q;)=e

l l A r r,NWet$-tvw rt n

6*-(l*,1",r+) = <q+ @+**l qi> scrJ = g\ 2t*t.@-qtfo@)Q-,.p.

Page 13: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

*r -S+tQ# "f**iaha- s-rr-fl.'+- tJ * _

ro- - -i-:-t:{z*r}e-{-"tr*e:"l__ Aelrt>o_ l-rl __

Jo

' 2

- yL Z\n1

2n2r&"eWL

- l

l . , ? a_. '

I

Page 14: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

Sthc-e, S#r{orn2f s nyg*x"*nn&nn ts v"L0r'ol

co(n & +V $ll'*t\ o{p?rg('Lo{i*^

roo r ao

\ a: u3"fzn H I rgi -J-J- f \

fo^ e1ns,

t-[n+'rl =vtl^

= tFt-r| I

{

lsl & (e1 *e

. t q

{bow\ t f l ) q11f4 .il

ft," ,t *Vt ,bt torg*,u.,€

=,ffi L61e-?h^ =*v*a,.= tf n

Re(") =tfn7 o

vA'

Z dU^n*t)

n\ = {t*t/"* v {%'r an(\""-n} :{r* €n@'rn

(3)' ("' &'aQ rL "+ 4L'6 ̂ 9fi'Aha't

\/

IUO -

2Lt/tt

Page 15: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

@

?roWm2

6 = tfN zAtt = eN =jt.N

opJ tl evav/ay $. &tt'r't d4^ifienn ++t* pnlagtk t

<# le-;fi L++-ath lqi) =

f ' rb r

l+l'" u4'xlr ,(/, . ../ "e x 4' 'f n-^

,#ileqi-"r] Dt e.+.

ffrr' =g2w.T;;r,te).t =? ) we Jividr 4k- Sror,{p {ra*&-

1,,+o +*o gr'af.s , 1q,., -..r4t^\& tqi",..riu.J

(y | "-'iw+'uh

l1;y = J\, exp1i

- k(E.J- [r,,. r1*, a,?i,ll \er;h e/ ) ' '

1-rr",<- ?1 .= fu,*(Nt-p'm)*Srypoe,a -lh",l Ln j's Nlr ,' so |h.rl-no{*s ttr, - .r1j-,,q1ftirr,..,,1,r-rJ rWe furLhe. hnue,

I ̂ r,. .. )1r, J1A1:nr .. . A1*

stlnGrlo

x "r @t {"i -1$n erP Lf L (t #' -','r]

t3l_V

"V

L4 :

- v

r L

{'n

Ee,rN J I

ie7(yq-'=j tr

Page 16: Ll,c1(e - Department of Physicsfiete/HW_3_Sol.pdf · knle&r"ncn1 Af* Qt"Gng Ll,c1(e W-n*orLtE-?wbfui"r L lre sb'l *ith $* Hubb-,./ H',,u\t*ooi*v (t, n' , 44, ezi) 4 t t lex*bot )

Usin6sJr$"ifirn 6ivan bI ?, P1 ,ff.* *g,r.o, [s1 ,ey]

{?l.-;nL++-u}tult;7 = Ia, ll, *rrl+t#*t,rll

\%, w L+f*' rrr,ilf :lh +0,(- c,^it ,l *a*, e+oJ

= frr mwt;W,-to,qrl ^ l,T,q[*f:.rtt,a]l= Jr, (1 { e Luut h* <14 1e-;frt*-t)hlq)

-2< nto,litX elP,oenh otre nu-L*s

= lOl u(tu,t{)t,lu (t,+ )Ii,d

* The *pp,-or,**h*1 *e-ut)4"* WIn3ranV,L. r{4 o1*,5t1 ,! lLe orv-

A\uT oo f,fi ,4 4+' u-lextbook ("*+t*Eo\Qu* *tW?**affd'",s1h.

t0