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$ *rxremt* N- 13. $il. $}*gr*e II N*r xmim *fi*nr, *Tlr n **^*.u,ly I {}fi gffi q* $$N$rxg ffimffi s*r$^qm$fi qpxx

&{ax. Mar:ks;1{}{}Nr**s;,I"" .z{r'rsn sr any IUyfi -fwttq*uc"*l.i*rn,1 sy scJ*c/fng

rrf Jeasf frvn rprrcrsr*rr*rs/rclrm e#c* p*it, {'

?" ,,$.rxe*plec wrfsufrg rS*Sr* srxfr*r&/y.

F'*xx'.{fu

Tirnr: "l hr"s.

ie

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4S.! r.

(;ohxn* ;\ . I30xxl5{.}u:r:: , c&r}'i*"r lln axi.au] i**d i?{)i} ki\i"(;olur:x: t} : ?.30x$S0mm, r.*rrir:s;rn axial l*atl l*0S kN,Rrrslri*t &e widrll of l.*i:ring {.n 1i.00 mrm. $BC *t sfiil is lst) kl,j/m?

Xr*f,S:etrVll*{ nrr: []ie r*tuil,Ernentr* r:f. * g**d ft:u:rdi*tion?Discuris tlle v*rrious mc:thods o{'irnprerving t}w t r;*ringlle*ign * r**tung,uinr cumt>ined. fi:*tir:g ftir coiu::*ns A{<lllou'in61 riata:

{{}4 hlarks}c;*prilcity *f's*i,ls. {{}6 n}xrk*}and B spaceei at 32.0$ mm c/c fr,lr the

{,I.{}'l!*arks}

{{}r{ &tark,ti0r *em*nl, nr*rku in lwci

{l$ Mxrk*}

{r}6 h{**"ks}

what is bE:nding ii: hric',kw*rk'l t/lrtt are th* e*nsicl*rntir:ns to l:r *n.sursd ft:rr g**rl i:londi*g1

l-)rsti*guisii ir(iw*r:n ll.*qiisli }-i*nd ;r*r:i f:'li:nrish hrirrrj" {(}{r i?larks}

{t}4 [,1*r'ks]

fhem witi: sket*hes. {t{l itxaykx}

{{}5 It$xrkx}

uncler.pinlling,

{05 Mxrkrlit{} lVf*rks)

{-'li:rpet'* tire $dvarriag*s; l*rrcl cli:ii:r1var:l:lgr:s *{'l'l;rt :r:*[is ov*r p:it*h*ri r6of,s. {11 kr*rk*}

:', t) t-l !'

{ I{} h.{*rtrr_r}

$)rtr{*Si:i [';i:sii'1n ;r iJl>g ieSlg*rJ stsir *as* ft:r a "iir*,

*r'sir.s: ?.Sfirxs.Sln Jrrr a {k:rr h*ig}:t ,of'3"i} m"I)rarv a l:cat slt*lch *I'pl*rr and **r:ti*nal. *k:v*Ii*n of a stair" {i*, M*rks}i-' wr"ile l:r ir:115' {}ll iu}Y lwo E:l' rlr* fnllowing. ,vitlr tre*t sketchcs: i) p**e Iled doorii; ( r:ilapsible i-1al.r* iiii iittv '.vir;rii:;v ir,) {.1*r:r:er wi*rJ<rw v) V*nli}at*r. {r$ t11$nrtr.s}

:i. \\iir;rt ari: r.it* icquir*rnr:n{.s *i,;r g***{ J:l*uk::i1)b i)escril:c ri:c ;:r*ui:r.llu* {eir urrr.vi*1t t_rut t:i:* piils.tcr.ing with i1m*L'i liiil--i.

il. i:r:iliain r-lrr--. prr:ccrlrrrc rrf y:aii:tir:g lilr iri.rn anrj strrr:i r*ru.f ac*s.

Deline'scafY'olding' and rnentit:n its,cornpon*nt par1s.Dcfinc 'un'Cerpinning' xnd lner*i*n sorne rl'th* situali*ns whi*ft rjemand

f )clinc: itn at'ch- fu{eutlor: i}:c vari*r.r$ *$rnp$}}{:r}t.n ris*ri rvitS n*r*{, skel;*llr;s^

Writc shlrt r_x.)I{:s fit}:ir. iilillurv cE.*icrr:ir* llltc.ks.0. urbiiir*r,1 r:::url hkr*ir_.;.

il. Ilrecast r"r:r ling *i*rn*r.l{s. (?{i &*xrkr}

tirurn ,\ i

a {t{iMxrks}h' \fitat is tlirlnp pr*ui"-*t>u:rs*? }:)x;:X*jn its ner;sssity in rr b.*ilding, i{}s l}-{*rtar}Lr. wtrat ir* {irc rr:rluirsrn*nls c:1, irl.:al r:ral*r:ii:r} fi:r rjnrn.p p,,*ot,n[i ;;; ;ffi;

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rsr feirsr TW{} rytrrssrnnspsrl errs.dl;:*rf.J";?fr-lxmg, d*t*. n,rr{rj $e $,^Lr'r{rfferf s**ir*s{p,.

$1,*,{$..$_;:*

h [][t'tt'is an nM(]S transistor fahricril*c'i Iixplain with ireat sJ<*tchcs. "

lil [|]:nlc' Wl:*t ix i: tvisii*t* iii,**rr*r1) I:.xplair), -""''"T-" rn$'

{$.} i},tark*}a' t)*r'ir'* f l^ir: un''4{)s^inv*ri"er ilc tha.a*tcris{.ic:; gi'rripirir:al{1,. {rlrn i:-d*vi*e .t ri-<jcvir:t:.*h;u"ac.t*r'i s li,;s ar:rci sh*.w u li rip* ri.rti * g re g i*nti.b. wirat is it n*ise *:;uxi:1f 'obtrrinJn*"va.rue,s r:f v:11., v*r, vs)L & v*u n-J--;,[THlur}:;lracti*ris I ics n {, * tlpi cal, in,,r*rt*r.c' Whi:t is iu""hl*st.tj dcsigrr'/ -vir*r.

i:lrirr IJle rrierits *n6 <l*:,*rits,1 {{}(i hlxrks)

{{}":X Mxrksi

{"}hiain thr:: sti*l< iiia,glr;xi:;lrtii lir1,,r.rLrL *f i.i twt:".r.lnv lss:lt:Ilcr.r,viIh t:r:;l]-ri*.

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{: rJ{ .

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{{}ti &,tnrlisi

{{J$ il{x v"lir:i

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{{}* M*rks}in terms *{'

i{}$ &t*rk*}5

-{"*}f,{-;;.ii\Vltiit llu'i: iire,: i;r::;1jjj1g, iiri:l*ri: {i:r- :

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{.; {} ,

ii.

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{}{i{-)v43

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+u*r*pi *t;. {{},i S:I:u"lr,*}

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S&wurs*,s,strffi,ff &sn,m,$Ss$s * $

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rn$thod. I::i consiar"rt.

ilr'*il tlt**l'01l1ii.*nel *l'cantiJqrver heayr: shorvn in Fig,Q.?{h) r.rsinlr m*ur*nt lur:*r

{{}(r i\tnrk*}

I I?- jcr,,r I IDHIV

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c.onr":**h";i{eci lo',rd for b*am trh*wn lu lr,ig"e.?{i;}, i.rsir:1{,'.'?(J0 x l{ir'le i{lu:} a,reJ i ,,.:, l*} rq rri",t ,r,.. "i}''{

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I:iir:r'.

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tl'r* t*1: +t'tli*tl{} &{r*rrkxi}

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lvhat ar"e tit* tr]elIIlaIi*r:t atljus;trnr::nt$ oJ'a tJ:r:*r]olits? Lixpia,in tj:* spire test."i'Jre {rilk:wirrg 0irs*r'ali*us u,*r* tak*,", *uiinrt tir*"**rr*g *i.duuiy:y ic'sr.itr:itr.{rrTt(:lt iji Sitil.li reatlin;.i',, nt

A

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{CI$*I*rksi

t:f radi*$ 5{)0rn- }J'the c}rnina;lc r:l'thc i.ntefsecrinn p*int is 1000.0m C,rlculafs fhe clir*r fbrs*tttrtg +Lti *tlrvo Lry l{arr.klne's <Jeflu{:tion iurp,le mcthod. l:ake the nonnhl i}i+rd ** ttl -. {t# Marks}

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ii) lt"sdius $iihe trrst arr: .'Z{}Ornii,ii ltadins o['th* ser:oniJ. ilr* *, tj{irnit') Chainruilc oflti:*: p,trint r:f,iniers**ti{lr1 *= I50rl.R{lrnvi I)*flr,:*:ti*r* *ngl*:'r:i'l}'r* fir"sl air* ", S{}.,

lii(1#r)Ii(:''i.

h' A rt''*.nt c*rv* Ail}} is tt> he set ex,ll i:etw*en t.w* parall*:i rtr:aights $0rr: apsrt 'f ?il*l}ffitl}h*lrvr:*r:r': twil rarl$*rlt p*jnI"$ ,\ *nrJ Ii] rs I2*r:i. Fi;r.iji 'i*!"rc **;:iius Id it'{{.1 ,", }{, *, qrij 'l'hr.l

rai,iir.rs l{2 ii'R1 ,=, 1{}{irn.Aiso r:alculatc th* lengtlts crf

'hrrth t,he al*s o'f r$verse cun,e, {{,, tut*rk^s}

a' Whert i$ i:l tl"iirlsiit,iil,t: curvt:? fixplair: f.hc r*qtlil'r:*:n*nts *f'a trlu:sitir>n clrr.c. {{}dr s.t*rku}

'":. \"\"r{,li rrt:;ll rik^*,tc}rr:s c,tplajn il:* iypcs {if, r.i.:r-firrr}l curr,*s. {{}6 ${*rks)

hJ " 1s{i*ttit,_,4r*'i* t:l zi:ti.r r;i:"cl* * 22{}il*,rr'. d.i;,rn*t*r,irtti* rnll*r,,,Zcrn, .f.}r* r,t:riter ivss

p:irr;t:,* hr:r,*rttj ih+ hrr.rH* nt a djlitrfnft: t)f'3crn.'I'I:* uru:x*; *ntrl*sr:sj hy vurii:lr*, **nr,r.-,r, ui*-.ii"** h+i*rr ',6

M*rk*-i

{*-rirtii,'rrll i;itiArila i,i:a;

I")*t+rrtrir:* {i:ru:,Jlirl;t{:.if,y *{' ti"r* re.:^slvoiF,prisu:r-ri*i*l and tr';rpe;lti**I r"ril*, l,4nt:r*: lh*

*$r+

if the {tll re**ruoir lr:vel isr'$l'Lrme helnrv Ii.. t, I{}*.0rn.

;1

l{l{ lri\l I ..,

s l*ii-,

r{t2t]3rl

l')(I i? ,.-,

:)5

I25^{}nr by b*{}r rhe{{}fl ibt*r,k$}

1 _.. t) ,\.!-. t1 t :,

,{

{}{}{"1\I4$

Xi'qlu*"th,$*:.r,xr*x{r*N- $$.5{. }}egree &Ix*tlx{snll iss}, "}u'ffi&*#uly ?tX}S

$ssrd rm xs $ $ m ax xx d F$}nc$x"m x* $ $ w ss mwr$N $ ss e.sIr4 a.-q. N{;,rr:ks;. I 0{.ii'iritr:: :i 1ri's"

Fiic.!$.*: .f, ..dru.srr*,r.lj, {o}$j,, f;.f $/f.l /tifJ ry*xnsff,*rr.E ss{sr.:Ifitgg af d*lrrsf I'W# !'rutnr r''*rr:lr p#rt'

?' '&'$l'r"s'frrg if*rr'i* rrf'*x* p'lrlrrtrr sg strdtrrrJ-rf1' rr't'si*ru**rr1*

,{ i:l .

i.iJ-

ff*S[.::t1!llist.inllr.iii;h b*ttt,*t.)Ir i.)tr)tli] ults:tt.ttcl ilti''v and pi1:* fltlw. {0;{ fr,Ialks}

;t: r:**ti,t11gulnr e,hu:nt:l *rn wiel* anri ,Iln"clecq has 3.*it}r:.lf I in 900. and is. iinoti x;it"}-i

iui:rr:;i$r: iir eii"r*hi:rr1:*;. i{}s tut*rht}

C.

"t

chann€i.rr is.hservcd in rhc ionn,Hon .f hvdrauric jurnp in a l.5m wirte recorg"r", *r*,S,i11 ,tti[ tl$.-

/;J:tl,:p*r ol flow bt{orc and after lhc-iump are ().1 5m aad I .2m rcspeorively. f ind thc dischsrge,Yex ,-#l/ '.

.riiical Jr2rtr arrrl loss oihead rr; ihc;rimp. (08 M!rk') \d;f// ;

JJlt/

li.;rliiit:ir {itr: i-rii*i:tiiiit-:til;lt t.tj \^"'iil.tir it;lirtttt.t:r" in pig:e:1. {ii'* '}'[*rk'si

c.

:t

i:

!r

.i iilr r .

\,!.'Jiut is lt.nVir:if,;1:'s ,nr*t,]ltd r:iilix ;r I *i rt: :trr:r * J.I -v {hr:,t?t I 1 i.r tt, :i;i S

ii il**r*t:l:r:i*sir::illlrttlq

d i n:t:nsi g lt il 1 n n i,ri yt i *? Ilxp I i*i r':'.'vi tlr ;itt *"c i:ll:R1)l e -

iil$ $artrrs)

{i.l$ ir,'l l*r}i*}Lt.

"b.

i i ) l'ir n*rri;* t ic: tiii:riIirity ii ii l.)-rr:irrni c sirr: i i artt\'

I iri rrg ISur-:i< ilr,lghilili' :l

i)1,,\; ,,,,, ,l-:lii:i ,O i iii Il

tiltr i.tl&rks)

H {}r*ilr*t:i rt}:*r,r, tirat tl:r.* v*lil*ity ttrrtrrrlir it cit'cul*t" r:il{.ii:* is give:n

i,., tlii: rirass) ij*r'rsri.\, iittti 1l is t,l:r:: iti:ttllilt'iilitltt titl{: i{.1

q i)'"i ,\,t urks]

*5fli#S'

iriri..:rit lftu axis r>l .1*t rlr*viit13 iir thcl tii:-et:ti*rt u{"i*t :s I(il?-T. tI{} l\'larks}

A ri:iir:n rvlr*.i':i irit:; ir:i lx: i.Jr::ii;*,:*i:i irrr th* iiiJl<iwirr.g c3ilta:

iltJ"'r't.:i- 1u ir'i:; iii.:r"'l:iti1l;i.:tl ' {i{tfli:l( \1'.

j''ii,:i i'r*itti irvi*ii;ii.rir: '"' -ii)l');fi"

spr:r::tt "'" ii{1{}

1'111'fi.

i{.iri"ir: r:f:'l*i. r.ititilrr.:t{..1t- ilit: rv}tr:*} tiiiur:r*1t;:r''""" i'r ii}i.lrrer-lll I i::t ll*r*iti;y ""'' $ (&"'i'

A.ssr-*t:* {),. ,,,', .qi' :;p*e:ij 1-p1llq3 "" {j.ri.i:. r {..1 1}t} }trrr"hs1

l,.,ll{}i"rt: I:'l is l}rq ir*ntj ca,usi:ig. t[tr* liltw- I"] is tlre rJi;ili:*t';r of

$.5

{}6CV45

il. A:$,:rnmcis turi:i*e has to b* ciesigned to give en overall orfi put of .t?5 KW under a head *fllilrn.'l'he r*tational specd is 700 qpm. Determine the main dimensions of tirerunnerr runnervrlne fflgk:s, a$*uming, iryctraulic loss*rs as I0Yo, fl*w rnti* 0" I 5, ratio of ii:ner t* s*t*rciia:neter:x (}.$, rati* of wjdtir. to dianrotsr ft{ $utlet'* (}.}, *vera}i efllciency as 0,$2, Areahh*ked try thickrress of r:un"ner v&nss is 0,5%, (1fl Mar*s)

*utl*r alid in,l*t and aI** spc*d *f th* turbins. Ilraw the v*lo*ity triangles, (I{} M*rk*}

ix lefins *pecific. spssrl r:f a hydr*ulic irirhinb. Derjve *n rxiuatirm firr specilir: spr:ed in tsn:rs*f t:perating speeri, p$wer'and licaci" (st ft{nrks)

h. Wtr*t is a eh,aft rube? Wh*t are its tun*tions? Write the ditibrent tlipe$ of dralt tube ak:ngrrriih sk*tcir*s. ({}S Mmrks)

{). $efi*e unitr spr:r:ci, *nit di*chi*rgr: nrNl urtit pilw*l. ilr:riv* the *xprc*sion fur thtvse t$rrns,(06lkl*rlr*)

h; A Kap,lan turhine wt:rking un{Xsr a head o{:2(}rn ctevelops l2t}00 KW. The *uter diarneter of*re qqqqer is 3.i* and innlr f,*IT!*o of the hub is t,?Sln. The guide blade an$le at the

,extr$ry.re edgs of:,ths:rulrner is 35o, fhe hydraulic Bnd overall efficiencies are 88% end 84%: : : i:r:. !:':":. : :- -: :-.

S rr, I)$liflr)i) Ma*o,metrjc efficien*yii) Meeilu"ni*ul e*[:ciencyiii) $v*r"trll *tfr*i*u*y. {*ti *I*rkr}

h. lVhut is prirning uiieentn{ilgal pu$},p anrj h*w it is dCIne? {*s;t**rlr*}c. Th* <lianteter of an irnpeller of a c€flh"ifugnt putnp at irilet and outlet are 3t)0mne and 600mni

resp*rtiveJy" 'I"he velocity of flow at outlet is ?nr/s and the vanss ttre $et hack *t an angle t:f45o at the fiutlet. I)*termirre the :liniinurn startin.g $pssd of tire pump if the manornefi:ic*fli*i*r:rcy i s ?il9'i'. {{}{i M*rrk*'}

***'$*

r i"i{

'l.imc: I hrs

h

s$MA"I',4I

$rqlq$x-t,h Sr*$xI*Il$;*r S*".F:. $*gs"** $,1x*nrxxixlmt**xa, Jxxur**"$'uty ?{}{}$

ffiwxgg,gs'ssxffir $?S &$rx*hmxwms$wffi -* MW Ms*. Ma**s: t*$

Fi g $.* ; ,$ rus l,uer r*my Jri $,.{l ./irrff {d *ss;$t'i$ s*^s, .t*r/xlr:*$mg

rss dcx*^tf 'flpy{} *pc*es$,J*srs.S*r** cmrJx 3:wri(.

$)A${.'$]*-"/\

',':,'..'',,',,,,,,Y.,,,.','''".,.T''',.',,,,',.,,,1

lliiirririlllilrr.......1................1.....--.... -1......-..........r.......... ......., ..-.............

r (i.

h

,l .,Sillvc -111. ,.. 7.y +.-lc'{ , ,v((}) * t} "

lJs* Rr^ing*-Kutta m*liit;lci o:['

icngtl: lt "'" tJ.?,^

l.ise Xili{ne's pn*ciictor *-*orrec.

{..lsing'Iayliy,,'o $eries rnetlrr:d *n fincl y(0.1'), -v((};2). {txt'il{trrks}

i.[vfuurth srricr lo s*lr,rc X =. x -h Y, y{S) *' 1 ril x *.. t}.2 rvith slr:p

t.r:r rur*thocl t* fir:d y at x '"'' 1.3.g, given $I^dx

I x i"o i*ii r- | *o:l*

l*it 6 .*i

l it-i ili-{it,i luliltt l-i-.Ll$1" j

fi)? llt*trksi

::: K -* 1f

) With,

Jri

ir

,'\pply q.:r.:t:r'*ri:l.tll $utr). {l}? lYtr*rks)

Find i.l-ie arraly{i* fi-r*cti*l"r (23 *'' 11 "l- iv if v ''' ,;)* (x .sin 3" + y ofir$ y}" (*6'F+I*rks}

rind ti:* irxlrg*: *l litr*:x 6rui:atr.lcl ts x ". rLXiri iirnd lin*s paraJ.l*1 t* y -* axis rffidrir' {ht:

iian:ili.:li"r'lLrljo:l u\' ':":' y"'r |}lllvl, trt:iti skrll*h. (*? Marks){*TMarks) .fnlJ@i.r-an:;ii::lmLllio:l u\r :::::: y"': i.}lllvl, trt:iti skrllt*t.

({}?

'\""\ !.$; .d-/ -.- \ \

",),.{:i\Iir rhr1r- f {.a} ,,,,,, ."1

*- i-lt*,|. ,1, , {fi$ ib{xrks}-i:L i :' c. i.

Stiil.rt {.-lirt:t:l:\,*s r*;irlti,* 'll'ir:e..rt'*rrt. }le:ltt:* i,'t' tll.h'':s"tvis* *va.luiite ..'

i (.'I

i...... . .....*......-..............-...---i+;1.1 [irr''{. 'tr.r !r1l .,, -i, ' {(}7 lbt*rks}

I

(u-r-l).

{(}{r Marl*}

{il7 Mcrkrri

{07 M:tri*s}

{fl* M*rkx'}

{$? Mxr[ir3

r

I

{fi$ib{xrksr@

.$ i].

u-

I)rt:r,e thi1r -l ,...ix),.,,, .,1""*" nion .

.r.i' . \t xxi:x1:r'*:is 1:ulyn*rtrial ,)x:i ' x? *ji:< I2

Cuir:putt: L*,r, l:'1, P:, [']. .l:ta l;*in14 it.r:iir

I;'it a 1:illirbolll ,,'*'' ii i i]x ; cx:, qll:tt:, 1. i ,,

:l- I ,,- ;1"

,.1'j il,{lr I j lli.)ht-ar* t!r* cu*{ l:it;nL *{'ci:rrc}itliil:t ;*

I , I i I j-i ;{t... .....*..i". .... -....,'i- *- - --1. . - .

l y i tr i { i lii:lr tt:li: :\ir:t h$s {ill.:r tir:Iri r":'i'tr.:1ts itnd *lttwi: s*}s *rr: *$. riift*r*nt c+1<lt,tt"ti" itotriirriil*ls;. rvi:ili ix ti:.* 'prr:h::[:ilit3; ilrot n

**l*ur and thc i;thcrplnr:ed r*ndt'rruly l:n. {{}7 &{r*rkx)

i n lul r:r.s u I' I....* gonci i:* pri I "l't:

*l u [ *Is.:itrt,ur:' s fi:rrt*u l*.

I,:itSK:-$$th*, ij*ta :I r I ir i r I'}" ]-i-]i "" ' .j-. .r:"".-.i,*.,: ""-1. ".::: . -.i ..: " .""i

I ii,ii i I {)::l!j i (}:{ii i"?-II i"$,i:1. i

iniJ thi: lierrs <:{ r*gr*ssi*n if :

i i : i -5

1- t l q-fTit1-l i-| ii I

o-l e i xz I tn { 1$l i,}l}Ii iilru*{:r$^ J"iv* tf'" 1}r**s $*t$ ilrf, r:t ont:tll.il'\, ljtr.r..r. n*lcu"rsi. if th* cu.pll &r*

\o *ul] is rlrt i; sij.fi,tc*r t:f sanr* coir.lull

I t:t"?

*. *el-l-l*,,i).&nnd*in v&ris,bi{i

h. 'I'he probahilitY il:trt a rnan

o1' l0 tl-Itl),n, nt:'rv n8eci (:0, i)1/{} yl:*trs^

o. ln a ni:rmai rii*trihr:tinu" 3i.xr

iit:tJ sta:nrJilrxi dev i iititln - giv*tl

ir. ,[ir:r] t]:e plr:h*l:ilil.v ihat irr Ir3ft

*r* h{,.aclx"

{}#:MAT:4 X

ii) Discrcte prgi:ability tiistribxtiun with an *xa^rnple' {0$ Mr*rk*i

*g*ri 60 wili live up tg ltl is 0.ir5, Wlrat is tle prohability that out

n:iacti1, 9. ii) at rhr* m**;1 q iii) irit lsn$t ?" will live up to {he ag*: *l{t}? *{xrks}

r:f'the itctrti: att: tltiicier 45 ;lnd $r)( *r* *ver 64' ilir-ld th* ul*i'lr]

ttrar A(0.5) "'' 6, tS anil A(l .4] ''- 0.4:l' {0? il{arks}

[o$i;e$ o{ a J:air coin bstw,o*n 45'X, anel 55?ir n{ t'}re otttc*mes

{flti h{*rt<x}

A rirncl+m sarnPle oi"

0,04 inch*s" 0rr tlrc[*v*l oi' signi iieat:cr.

{{}7 Mark*}elistribut*d tv*r

"},lftLjY.4,

{$7 Mxrks}

b. A '*cc.hanist.

ix xr*king, ensine p*r1s tvil.ir irxlc ilianrslrtt' r:l'ii."i irrch*s'

l* ;:;tris show**l u ,*,.*** rii, rt.,{"li incl"t*s- '"vith, il stttnc}iird dr:viaii*n ()l

h*s,i.r *f thi$,$*Irrlill*, un* lt h* c*ncittd*<i thar lhe w*rk ix in,fbri*r itt 5t%

c. l;*r ]rr*, i$lll:ri,,ing deta {est t}r* itypothesis that the acc'idents are uniform'iy

irl[ t}:r* *itri''* t:f thu r't'*eil firr 9t% *orl{it}*n**'

i:linr"i i** --

t"L{ir,tgiir*1 tj i s tr: j L:i.r1,i t: rt * {' x

Mlargir:a.l distrii:*ii*n * l' 3r

{i*v (x,3i) if ,tifr* i*int' Bc{t'*{:x arrc* y is

b.[:ine*'ih* fisx*d proh*hililv'?**.r-*rr:{"r*g*l;w sfi:'*hnsti* xrentrix

i-i:.:; ir."1:: ii.]:j i

i'\ ::^r i)

1\1I'|i{I I i.,/ l

i . .,,+

A r:,*lrrp*ny *,t**:liti't'* *ha::g*x i.ris *;rr {jrr*l}r yrlar, Ii: h* hat lt *xri:l'or tft nrakc t"]" if ire i:*s{.rl nr*k* I{^ ll*r::t r:t*i';* t.} he *l:rnngr:'s

3tr*lf:t:*:tr:* ti.) (:hitliy-(: lllr(lt'L* lt:ii.li* A Crr nl*k* f:i *ifr:^ il'irc h;id rl

iind rii* nroh*hi'litl'th*l lr* wili irirvt: i;r rtli i:1"i,\ lnnkr: '4 rn ':{ili}'

{1, i{

{i){r kE,arl<-*1

(ii? &{rlrk*}

oIr*aki,. A, hr: chariges o'l'er

i:*^r '(-l' thc:il l:t: giv*s *qwl}*l*'+i rn*kr: Ll in -r'c{ir.3t}t}$ii) rr"rak* 'C' in 2i)10"

{t}? !\{xrkxl

,.F d. *. .$ +

I

/

i---r-r- f -1 l- T- | - -t- i

ir$;Ni i I i I I , ,-l_l II".* -1. --- i".* "' l- - -l- "-L-'-"-r"--t

$i*uxs.$:$x q:r!$es:* s' HS.ffi . s3*gs:** $IXttxx'xtmal$i*lx,

&Swm mmms &$ w'*$*mmw. $ws

kIA:tr"$xxld**

J'qlxl**.5.wlY 1'{}$$ss* ffis

Milx" h4 *rks: I {i()i'rirti^:: -i itl"s.

N*rt*; ,4$"wrsrrr r*s'ry '$rf $/elJe*CX x3lxcssinrut

s r.r {,i. ,r }?r r"r il*il /,, ffi,. r,r, ar* t}i* crire*tinn *osincs q:f ttr* lines *P & sQ anc{ $ he lh* xngl*tr tt

[-i-"']J',-i:]

"i,*T,'-;"I';;;

;;,]f,'"'i"l'--, $? #r' ] n n' Aiso d.*rive the cr:*clitiun itr the

p*r3:eudi*i'rli*:it-y ol'$F -$r {}Q (*7 Mxr}is}

t}. i:intl th* *r1us*1iltt r:f.t}re .pian.*,n*i.i:'ir:}: i}I,}xi$l*s r,lr.r*r.ttr1h t}:* ptli.rr't {,}, *.}, i) nrrd is

i) ll*rr*i:l*'t t* th** pk'rn* ?-x "+' ]ll + 5:r''s'$ -* t)'

ii) P*tp*ndl*ttlar trt ilre pliure', ?* ' y -r- 2x *''6 nlid 3x + $y ^ sZ * &' {{}? M*trkr}

r, lli*6 tt,le r:r;u*ti*i:x tr:: th* trvr: ;:Lr*rr:s r'l'hich his*t:ts tho angl** br:twe*r: th* plitnes

3x. *- -{y '*- {7 *"' } ru:ei 5:i 't 3Y -'4' "' }' {(}$ Mlrr:ksi

the plan*sul. a plrurc piissing ttx*ngh th1 line of inr*rsection l"f

an*l 'r** -t 3'y *:g""r 11 "'*' fi *uttl pet'pre*dieul*r ts then il. ()bt,;rin dr* cq**ti*lr

'?.... ,{., ^t... ?"r a- tr6 '* 0/il*-TrY I ta-

i'- Y -?i:-(i"''{)"

:). ,,,, --.,1. -... 1' ;igr.1!

-,1 '* ..) I

lr,

(:"

:Y *.-I

=,. !1.:.] ,,,. :{*- :l^.

') "...-

q ').;r

'- -i

;,;'ir:lsl th$ ertrutrli*ri t:t'l!:r* t'irit) $tsili$hr llrmtl thr*ugh tire *u:ip'ir-r *;tq:h.o{ rvtrieh

stririgl:t line, l,li(x *- 3) "" ,i * 3'*' r, anii it is inclitli:<J ;ri *n rmgle of {i{)" to tt'

l*ilrcl th* rnilgniii.rd* rlrr{ th* *qrlalti*n o{: il:e sliortest- clisti'uree b*twcen

plnr:*

{t}? hfarkx}

int*r:s**ts tl:*({}? h'1*rks

the li

{S(: lvXs}rks}

-* -*--*F

.,f. ,ii,,.,i i ]j *,-i]r. lt,**-i^+.tj-rl*. i::*3i -r- i Fi:r:rl i) sur:h tl:rsrf A -i I'H is 1:eri:enrti*ul;rr tqt

i-l . Al,;,.,, 'linqj thtl tir;t pr*rluct tf ;\ rcrith Li anti .\.($ "" {"1}' {ttY ktrtrks}

lf" ;ii ,,.,, gl -i.].i $ k , ii,* ?i -.i-r- ilii flncl ii r**it v*r:t*:r p*'rpe'ndit''uiar rn the plane r:*r'r1airli*g

L,*r^1: }\ & 1{ Ais*, str*w tlutr A i:i r:st p*ql*nrii+trlar U: 11 ' {{}? M'*rks}

t]"

Fil"l*1 thr: (:r.:r'lstxnt rr sur:|r {hi:'t" l}t*

J\ij'=' I ii "i 4j + k itrtl t:r:Pl*uitr'

r{ pirrti*l*: n:l(}\re$ $:ltll}g * ui}l:vix H '* t:'**

S*rcruni n:* i ts rr*lu*it,y it*t} ;x* *ul *rniion

vtx)t{}rs Afi "= ai - 5j *'2k , AI} * *7i * }4j'-' 3k '

{{Xi ${*rks)

., '} ..* cts.}t, r,',., 2.$in}t rvh*re t is tlre lifi::q: variglhl(.

ve**:rs *r}d als6u Jrnti tll* magnitucles *l'v*fu:tity elnd

iecu*l*rati$fi at {:::: {"},

$:ir:qt {hr: elir**q.ir.il*} elerii.,irtive ti i:{xyr.) =' xy= *" y:r'J at t'he p*itll (?, -'i ' l') in the

t5* r,:s:ot{ir I +'11,1 li -:..K.. Alsr:. tL.nrJ u5x riir**'[ii:rr ;it1*ug whit]: it is maxiln.ufi'

Pr*rl*-{}rii{ Vrr} '-'- '7..rr ?' }t rvh*r't: fi '* xi "{'}* -!'r''k l'xlil r "'l l{ l'

a. i:'t>r w.h*i u*1ur e;'i]' tl**:i ttiis vct:ltr1 p "-t*,r', t-r'*)i o i*y'" -*')if '"{Zoy* :l*?v2iK

Iri.l.t e.tlru ctivt:ry,t:trt:e' Alx* trnii V;< li ' {{}? ht$rhc}

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