Relative Motion Theory_E

8/12/2019 Relative Motion Theory_E

1/20

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"ckmnsleuckrplysnds.nm" ;

P A VNW CBVNBM

; PIAKVNWI CBVNBMCbtnbm ns k dbc`nmif prbpirty bg tli bòidt umfir stufy ks wiaa ks tli b`sirvir. Nt ns kawkys riaktnvi 5 tliri

ns mb sudl tlnmj anei k`sbauti cbtnbm br k`sbauti rist. Cbtnbm ns kawkys fignmif wntl rispidt tb km b`sirvir

br rigirimdi grkci.

Pigirimdi grkci ?

Pigirimdi grkci ns km kxns systic grbc wlndl cbtnbm ns b`sirvif kabmj wntl k dabde kttkdlif tb tli kxns, tb

ciksuri tnci. Pigirimdi grkci dkm ì stktnbmkry br cbvnmj.

Tuppbsi tliri kri twb pirsbmsK kmf @ snttnmj nm k dkr cbvnmj kt dbmstkmt spiif. Vwb stktnbmkry pirsbms Dkmf F b`sirvi tlic grbc tli jrbumf.

K@

DF

Liri @ kppikrs tb ì cbvnmj gbr D kmf F, ùt kt rist gbr K. Tncnakray D kppikrs tb ì kt rist gbr F ùt cbvnmj

`kdewkrf gbr K kmf @.

0 PIAKVNWI CBVNBM NM BMI FNCIMTNBM ?0.; Piaktnvi Xbsntnbm ?

Nt ns tli pbsntnbm bg k pkrtndai w.r.t. b`sirvir.

Nm jimirka ng pbsntnbm bg K w.r.t. tb brnjnm ns xK

kmf tlkt bg @ w.r.t. brnjnm ns x@

tlim Xbsntnbm bg K w.r.t.

@ xK@

ns

xK@3 xK x@

x@

xK

xK@

@Brnjnm K

Ixkcpai ;. Tii tli gnjuri (tkei +vi fnridtnbm tbwkrfs rnjlt kmf vi tbwkrfs aigt)

Gnmf x@K

, xDK

, xD@

, xK@

kmf xKD

.

6c

K @ D

brnjnm

;8c

7c

Liri, Xbsntnbm bg @ w.r.t. K ns 6 c tbwkrfs rnjlt . (x@K

3 +6c)

Xbsntnbm bg D w.r.t. K ns ;8 c tbwkrfs rnjlt . (xDK

3 +;8c)

Xbsntnbm bg D w.r.t. @ ns 7 c tbwkrfs rnjlt (xD@

3 +7c)

Xbsntnbm bg K w.r.t. @ ns 6 c tbwkrfs aigt. (xK@

3 6 c)

Xbsntnbm bg K w.r.t. D ns ;8 c tbwkrfs aigt. (xKD

3 ;8c)

0.0 Piaktnvi WiabdntyFignmnt nbm?Piaktnvi viabdnty bg k pkrtndai K wntl rispidt tb @ ns fignmif ks tli viabdnty wntl wlndl K

kppikrs tb cbvi ng @ ns dbmsnfirif tb ì kt rist. Nm btlir wbrfs, nt ns tli viabdnty wntl wlndl K

kppikrs tb cbvi ks siim `y @ dbmsnfirnmj ntsiag tb ì kt rist.

MBV I ; ? Kaa viabdntnis kri riaktnvi & lkvi mb snjmngndkmdi umaiss b`sirvir ns spidngnif. Lbwivir, wlim wi sky

viabdnty bg K, wlkt wi cikm ns , viabdnty bg K w.r.t. jrbumf wlndl ns kssucif tb ì kt rist.


2/20

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"ckmnsleuckrplysnds.nm" 0

Piaktnvi viabdnty nm bmi fncimsnbm -

Ng xK

ns tli pbsntnbm bg K w.r.t. jrbumf, x@

ns pbsntnbm bg @ w.r.t. jrbumf kmf xK@

ns pbsntnbm bg K w.r.t. @ tlim wi

dkm sky vK

3 viabdnty bg K w.r.t. jrbumf 3ft

fxK

v@

3 viabdnty bg @ w.r.t. jrbumf 3ft

fx@

kmf vK@

3 viabdnty bg K w.r.t. @ 3

ft

fxK@3 )xx(

ft

f@K

3ft

fxK

ft

fx@

Vlus

vK@

3 vK

v@

M B V I 0 . ? Wiabdnty bg km b`oidt w.r.t. ntsiag ns kawkys zirb.

Ixkcpai 0. Km b oidtK ns cbvnmj wntl 9 c/s kmf @ ns cbvnmj wntl 08 c/s nm tli skci fnridtnbm. (Xbsntnvi x-kxns)

(n) Gnmf viabdnty bg @ wntl rispidt tb K.

(nn) Gnmf viabdnty bg K wntl rispidt tb @

Tbautnbm ? (n) v@

3 +08 c/s vK

3 +9 c/s v@K

3 v@

vK

3 +;9 c/s

(nn) v@

3 +08 c/s, vK

3 +;9 c/s 5 vK@

3 vK

v@

3 ;9 c/s

Mbti ? v@K

3 vK@

Ixkcpai 4. Vwb b oidts K kmf @ kri cbvnmj tbwkrfs ikdl btlir wntl viabdntnis ;8 c/s kmf ;0 c/s rispidtnviay

ks slbwm.

(n) Gnmf tli viabdnty bg K wntl rispidt tb @.

(nn) Gnmf tli viabdnty bg @ wntl rispidt tb K

Tbautnbm ? vK

3 +;8 , v@

3 ;0

(n) vK@

3 vK

v@

3 (;8) (;0) 3 00 c/s.

(nn) v@K

3 v@

vK

3 (;0) (;8) 3 00 c/s.

0.4 Piaktnvi KddiairktnbmNt ns tli rkti kt wlndl riaktnvi viabdnty ns dlkmjnmj.

kK@

3ft

vf K@3

ft

fvK

ft

fv@3 k

K k

@

Iquktnbms bg c btnbm w lim riakt nvi kddiairkt nbm ns db mstkmt.

vria

3 uria

+ kria

t

sria

3 uria

t +

0

;k

ria t0

v0ria

3 u0ria

+ 0kria

sria


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0.6 Wiabdnty bg Kpprbkdl / TipkrktnbmNt ns tli dbcpbmimt bg riaktnvi viabdnty bg bmi pkrtndai w.r.t. kmbtlir, kabmj tli anmi obnmnmj tlic.

Ng tli sipkrktnbm ns fidriksnmj, wi sky nt ns viabdnty bg kpprbkdl kmf ng sipkrktnbm ns nmdriksnmj, tlim

wi sky nt ns viabdnty bg sipkrktnbm.

Nm bmi fncimsnbm, snmdi riaktnvi viabdnty ns kabmj tli anmi obnmnmj K kmf @, limdi viabdnty bg kpprbkdl

/ sipkrktnbm ns sncpay iquka tb ckjmntufi bg riaktnvi viabdnty bg K w.r.t. @.

Ixkcpai 6. K pkrtndaiK ns cbvnmj wntl k spiif bg ;8 c/s tbwkrfs rnjlt kmf kmbtlir pkrtndai @ ns cbvnmj kt spiif

bg ;0 c/s tbwkrfs aigt. Gnmf tlinr viabdnty bg kpprbkdl.

Tbautnbm ? WK

3 +;8 , W@

3 ;0 WK@

3 WK

W@ ;8 (;0) 3 00 c/s

snmdi sipkrktnbm ns fidriksnmj limdi Wkpp

3 |WK@

| 3 00 c/s

Kms. ? 00 c/s

Ixkcpai 9 K pkrtndai K ns cbvnmj wntl k spiif bg 08 c/s tbwkrfs rnjlt kmf kmbtlir pkrtndai @ ns cbvnmj kt k

spiif bg 9 c/s tbwkrfs rnjlt. Gnmf tlinr viabdnty bg kpprbkdl.

Tbautnbm ? WK

3 +08 , W@

3 +9

WK@

3 WK

W@

08 (+9) 3 ;9 c/s

snmdi sipkrktnbm ns fidriksnmj limdi Wkpp

3 |WK@

| 3 ;9 c/s

Kms. ? ;9 c/s

Ixkcpai 7. K pkrtndai K ns cbvnmj wntl k spiif bg ;8 c/s tbwkrfs rnjlt, pkrtndai @ ns cbvnmj kt k spiif bg

;8 c/s tbwkrfs rnjlt kmf kmbtlir pkrtndai D ns cbvnmj kt spiif bg ;8 c/s tbwkrfs aigt. Vli sipkrk-

tnbm ìtwiim K kmf @ ns ;88 c. Gnmf tli tnci nmtirvka ìtwiim D ciitnmj @ kmf D ciitnmj K.

;8c/s

;88c

;8c/s

;8c/sK

D

@

Tbautnbm ? t 3DkmfKbgW

DkmfKìtwiimsipirktnbm

kpp

3);8(;8

;88

3 9 sid.

Kms. ? 9 sid.

Mbti ? kkpp 3 kppvft

f

, ksip 3 sipvft

f

vkpp

3 ftkkpp , vsip3 ftksip


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Ixkcpai :. K kmf @ kri tlrbwm virtndkaayupwkrf wntl viabdnty, 9 c/s kmf ;8 c/s rispidtnviay(j 3 ;8 c/s0. Gnmf

sipkrktnbm `itwiim tlic kgtir bmi sidbmf

Tbautnbm ? TK

3 ut 0

;jt0

3 9t 0

; ;8 t0

3 9 ; 9 ;0

3 9 9 3 8

T@

3 ut 0

;jt0 . 3 ;8 ;

0

; ;8 ;0 3 ;8 9 3 9

T@

TK

3 sipkrktnbm 3 9c.

Kantir ?

@Kk

3 @k

Kk

3 (;8) (;8) 3 8

Kasb @Kv 3 @v

Kv 3 ;8 9 3 9 c/s

@Ks

(nm ; sid) 3 @Kv

t

3 9 ;

3 9 c

Fnstkmdi `itwiim K kmf @ kgtir ; sid 3 9 c.

Ixkcpai


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Ixkcpai >. Vwb dkrs D;

kmf D0

cbvnmj nm tli skci fnridtnbm bm k strknjlt snmjai akmi rbkf wntl viabdntnis ;0 c/

s kmf ;8 c/s rispidtnviay. Zlim tli sipkrktnbm ìtwiim tli twb wks 088 c D0

stkrtif kddiairktnmj

tb kvbnf dbaansnbm. Zlkt ns tli cnmncuc kddiairktnbm bg dkr D0sb tlkt tliy fbmt dbaanfi.

Tbautnbm ? Kddiairktnbm bg dkr ; w.r.t. dkr 0

0;0; kkk

3;D

k

0D

k

3 8 k 3 (k)

0;u

3 ;u

0u

3 ;0 ;8 3 0 c/s.

Vli dbaansnbm ns oust kvbnfif ng riaktnvi viabdnty ìdbcis zirb oust kt tli cbcimt tli twb dkrs ciit

ikdl btlir.

n.i. v;0

3 8 Zlim s;0

3 088

Mbw v;0

3 8, 0;u

3 0 , 0;k

3 k kmf s;0

3 088

0;0v 0

;0u 3 0k;0s;0

8 00 3 0 k 088 k 3;88

;c/s0 3 8.; c/s0 3 ; dc/s0.

Cnmncuc kddiairktnbm miifif `y dkr D03 ; dc/s0

4 . PIAKVNWI CBVNBM NM VZB FNCIMTNBMKr

3 pbsntnbm bg K wntl rispidt tb B

@r

3 pbsntnbm bg @ wntl rispidt tb B

K@r

3 pbsntnbm bg K wntl rispidt tb @.

@KK@ rrr

(Vli vidtbr suc @K rr

dkm i fbmi `y akw bg kffntnbm br risbautnbm citlbf)

ft

)r(f K@

3ft

)r(f K

ft

)r(f @

.

@KK@ vvv

ft

)v(f K@

3ft

)v(f K

ft

)v(f @

@KK@ kkk

Ixkcpai ;8. Bòidt K kmf @ `btl lkvi spiif bg ;8 c/s. K ns cbvnmj tbwkrfs Ikst wlnai @ ns cbvnmj tbwkrfs

Mbrtl stkrtnmj grbc tli skci pbnmt ks slbwm. Gnmf viabdnty bg K riaktnvi tb @ ( K@v

)


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Tbautnbm ? Citlbf ;

K@v

3 Kv

@v

K@v

3 ;80

Citlbf 0

Kv

3 ;8 n , @v

3 ;8o

K@v

3 Kv

@v

3 ;8 n ;8o

K@v

3 ;80

Mbti ? @K vv

3 dbsvv0vv @K0@

0K

, wlirins kmjai `itwiim Kv

kmf @v

Ixkcpai ;;. Vwb pkrtndais K kmf @ kri prboidtif nm knr. K ns tlrbwm wntlk spiif bg 48 c/sid kmf @ wntl k spiif bg 68 c/sid ks

slbwm nm tli gnjuri. Zlkt ns tli sipkrktnbm `itwiim tlic

kgtir ; sid.

94 4:K

@

48

68

Kv

@v

Tbautnbm ? K@k

3 Kk

@k

3 jj

3 8

K@v

3 00 6848 3 98

sK@

3 vK@

t 3 98 t 3 98 c

Ixkcpai ;0. Km baf ckm kmf k `by kri wkaenmj tbwkrfs ikdl btlir kmf k `nrf ns gaynmj bvir tlic ks slbwm nm tli

gnjuri.

;7 c/s

4:

;0 c/s

`nrf

08c/s

@by ;7 c/sVrii

0c/s

baf pirsbm

o

n

(;) Gnmf tli viabdnty bg trii, `nrf kmf baf ckm ks siim `y `by.

(0) Gnmf tli viabdnty bg trii, `nrf kmf `by ks siim `y baf ckm

(4) Gnmf tli viabdnty bg trii, `by kmf baf ckm ks siim `y nrf.

Tbautnbm ? (;) Zntl rispidt tb by ?

vtrii

3 ;7 c/s () br ;7 n

v`nrf

3 ;0 c/s ()br ;0o

vbaf ckm

3 ;< c/s () br ;< n


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"ckmnsleuckrplysnds.nm" :

(0) Zntl rispidt tb baf ckm ?

v@by

3 ;< c/s () br ;< n

vVrii

3 0 c/s () br 0 n

v@nrf

3 ;< c/s () kmf ;0 c/s () br ;< n + ;0o

(4) Zntl rispidt tb @nrf ?

vVrii

3 ;0 c/s () kmf ;7 c/s () br ;0o ;7 n

vbafckm

3 ; < c / s () kmf ;0 c/s () br ;< n ;0 o

v@by

3 ; 0 c / s (). br ;0o

4.; Piaktnvi Cbtnbm nm AngtXrboidtnai cbtnbm nm k angt cbvnmj wntl kddiairktnbm k upwkrfs

(;) Nm tli rigirimdi grkci bg angt, kddiairktnbm bg k griiay gkaanmj b`oidt ns j + k

(0) Wiabdnty kt ckxncuc linjlt 3 u dbs

(4) V 3kj

snmu0

(6) Ckxncuc linjlt (L) 3)kj(0

snmu 00

(9) Pkmji 3kj

0snmu0

Ixkcpai ;4 K angt ns cbvnmj up wntl kddiairktnbm k. K pirsbm nmsnfi tli angt tlrbws tli

`kaa upwkrfs wntl k viabdnty u riaktnvi tb lkmf.

(k) Zlkt ns tli tnci bg ganjlt bg tli `kaa2

(`) Z lkt ns tli ckxncuc linjlt rikdlif `y tli `kaa nm tli angt2

Tbautnbm ? (k) @Ak

3 @k

Ak

3 j + k

s

3 u

t +0

;@Ak

t0

8 3 uV 0

;(j + k)V0

V 3)kj(

u0

(`) v0 u0 3 0 ks

8 u0 3 0(j + k) L

L 3 )kj(0

u0


8/20

XL^TNDT

"ckmnsleuckrplysnds.nm"

? Cbtnbm bg swnccir gbr b`sirvir

? Cbtnbm bg swnccir gbr b`sirvir

6 .4 Pnvir prbàic nm twb fncimsnbm drbssnmj rnvir ?Dbmsnfir k ckm swnccnmj nm k rnvir wntl k viabdnty bg CPv

riaktnvi tb rnvir kt km kmjai bg wntl tli

rnvir gabw

Vli viabdnty bg rnvir ns WP

kmf tli wnftl bg tli rnvir ns f

Cv

3 CPv

+ Pv

Cv

3 (vCP

dbsn + vCPsnmo ) +vPn

Cv

3 (vCP

dbs+ vP

) n + vCPsnmo

f

x

WCP

WP

WC

y

x

Liri vCP

snm ns tli dbcpbmimt bg viabdnty bg ckm nm tli fnridtnbm pirpimfnduakr tb tli rnvir gabw.Vlns dbcpbmimt bg viabdnty ns rispbmsnài gbr tli ckm drbssnmj tli rnvir. Limdi ng tli tnci tb drbss

tli rnvir ns t , tlim

t 3yv

f3 snmv

f

CP

FPNGVNt ns fignmif ks tli fnspakdicimt bg ckm nm tli fnridtnbm bg rnvir gabw. (sii tli gnjuri).

Nt ns sncpay tli fnspakdicimt kabmj x-kxns, furnmj tli pirnbf tli ckm drbssis tli rnvir. (vCP

dbs + vP

) ns tlidbcpbmimt bg viabdnty bg ckm nm tli fnridtnbm bg rnvir gabw kmf tlns dbcpbmimt bg viabdnty ns rispbmsn ai gbr frngt

kabmj tli rnvir gabw. Ng frngt ns x tlim,

Frngt 3 vx t

x 3 (vCPdbs+ vP) snmvf

CP

6.6 Drbssnmj tli rnvir nm slbrtist tnciKs wi embw tlkt t 3

snmvf

CP

. Daikray t wnaa ì cnmncuc wlim 3 >8 n.i. tnci tb drbss tli rnvir

wnaa ì cnmncuc ng ckm swncs pirpimfnduakr tb tli rnvir gabw. Zlndl ns iquka tb

CPv

f.

6.9 Drbssnmj tli rnvir nm slbrtist pktl, Cnmncuc FrngtVli cnmncuc pbssn ai frngt ns zirb. Nm tlns dksi tli ckm swncs nm tli fnridtnbm pirpimfnduakr tb tlirnvir gabw ks siim grbc tli jrbumf. Vlns pktl ns embwm ks slbrtist pktl

liri xcnm

3 8 (vCP

dbs+ vP

) 3 8

br dbs3 CP

P

v

v

snmdi dbs ns vi, = >8 , n.i. gbr cnmncuc frngt tli ckm cust swnc kt sbci kmjai wntl tlipirpimfnduakr nm `kdewkrf fnridtnbm.

Zliri snm3CP

P

v

v

3

CP

P;

v

vdbs

CP

P

v

v1 ; n.i. v

P1 v

CP

n.i. cnmncuc frngt ns zirb ng kmf bmay ng viabdnty bg ckm nm stnaa wktir ns jriktir tlkm br iquka tb tli viabdnty bg

rnvir.


10/20

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"ckmnsleuckrplysnds.nm" ;8

Vnci tb drbss tli rnvir kabmj tli slbrtist pktl

t 3snmv

f

CP

30

P0CP Wv

f

WCPWC

WP

Mbti ? Ng v

P = v

CP t l i m n t n s m b t p b s s n ` a i t b l k v i z i r b f r n g t . N m t l n s d k s i t l i c n m n c u c f r n g t

( d b r r i s p b m f n m j t b s l b r t i s t p b s s n ` a i p k t l n s m b m z i r b k m f t l i d b m f n t n b m g b r c n m n c u c f r n g t

d km ` i p r bv if t b ` i d b s 3 P

CP

v

vb r snm 3

P

CP

v

vg b r c n m n c u c ` u t m b m z i r b f r n g t .

Ixkcpai ;9. K 688 c wnfi rnvir ns gabwnmj kt k rkti bg 0.8 c/s.K `bkt ns sknanmj wntl k viabdnty bg ;8 c/s wntl

rispidt tb tli wktir, nm k fnridtnbm pirpimfnduakr tb tli rnvir.

(k) Gnmf tli tnci tkeim `y tli `bkt tb rikdl tli bppbsnti `kme.

(`) Lbw gkr grbc tli pbnmt fnridtay bppbsnti tb tli stkrtnmj pbnmt fbis tli `bkt rikdl tli bppbsnti

`kme.

(d) Nm wlkt fnridtnbm fbis tli `bkt kdtukaay cbvi, wntl rnvir gabw (fbwmstrikc).

Tbautnbm ?

(k) tnci tkeim tb drbss tli rnvir

t 3yv

f3

s/c;8

c6883 68 s Kms.

( ) frngt (x) 3 (vx)(t) 3 (0c/s) (68s) 3 8 + snm-;

cP

r

vv 3 >8 + snm;

94 3 >8 + 4:

3 ;0: w.r.t. tli rnvir gabw br 4: w.r.t. pirpimfnduakr nm `kdewkrf fnridtnbm Kms.

( ) Pisuatkmt viabdnty wnaa `i vc

3 0P

0cP vv 3 00 49 3 6 ec/lr

kabmj tli fnridtnbm pirpimfnduakr tb tli rnvir gabw.

(d) tnci tkeim tb drbss tli

t 30P

0cP vv

f

3

lr/ec6

ec;3

6

;l 3 ;9 cnm

Ixkcpai ;:. K ckm wnslnmj tb drbss k rnvir gabwnmj wntl viabdnty u oucps kt km kmjaiwntl tli rnvir gabw.

(n) Gnmf tli mit viabdnty bg tli ckm wntl rispidt tb jrbumf ng li dkm swnc wntl spiif v nm stnaa wktir.(nn) Nm wlkt fnridtnbm fbis tli ckm kdtukaay cbvi.

(nnn) Gnmf lbw gkr grbc tli pbnmt fnridtay bppbsnti tb tli stkrtnmj pbnmt fbis tli ckm rikdl tli

bppbsnti `kme, ng tli wnftl bg tli rnvir ns f. (n.i. frngt)


11/20

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"ckmnsleuckrplysnds.nm" ;;

Tbautnbm ? (n) vCP

3 v , vP

3 u

Cv

3 CPv

+ Pv

Wiabdnty bg ckm , vC

3 dbsuv0vu 00 Kms.

(nn) tkm3

dbsvu

snmvKms.

PCPC vvv

(nnn) (v snm) t 3 f

t 3snmv

f

x 3 (u + v dbs) t

3 (u + v dbs)snmv

fKms.

Ixkcpai ;


12/20

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Ixkcpai ;> Km kirbpakmi ganis kabmj k strknjlt pktl K tb @ kmf riturms `kde kjknm. Vli fnstkmdi `itwiim K kmf

@ ns kmf tli kirbpakmi cknmtknms tli dbmstkmt spiif v w.r.t. wnmf. Vliri ns k stikfy wnmf wntl

k spiif u kt km kmjaiwntl anmi K@. Fitircnmi tli ixprissnbm gbr tli tbtka tnci bg tli trnp.Tbautnbm ? Tuppbsi pakmi ns brnimtif kt km kmjaiw.r.t. anmi K@ wlnai tli pakmi ns cbvnmj grbc K tb @ ?

Wiabdnty bg pakmi kabmj K@ 3 v dbs udbs,

kmf gbr mb-frngt grbc anmiK@

v snm3 usnm snm3v

snmu

tnci tkeim grbc K tb @ ? tK@

3 dbsudbsv

Tuppbsi pakmi ns brnimtif kt km kmjaiw.r.t. anmi K@ wlnai tli pakmi ns cbvnmj grbc @ tb K ?

'

viabdnty bg pakmi kabmj @K 3 vdbs+ u dbskmf gbr mb frngt grbc anmi K@

vsnm3 usnm

snm 3v

snmu

3

tnci tkeim grbc @ tb K ? t@K

3 dbsudbsv

tbtka tnci tkeim 3 tK@

+ t@K

3 dbsudbsv

+

dbsudbsv

3

0000

dbsudbsv

dbsv0

3 00

0

00

uv

v

snmu;v0

.

Ixkcpai 08. Gnmf tli tnci km kirbpakmi lkvnmj viabdnty v, tkeis tb gay krbumf k squkri wntl snfi k ng tli wnmf ns

`abwnmj kt k viabdnty u kabmj bmi snfi bg tli squkri.

Kmswir ? 00 uv

k0

00 uvv

Tbautnbm ?

K @

DF

v 3 uwnmf

Wiabdnty bg kirbpakmi wlnai gaynmj tlrbujl K@ v 3v+uKv

K3 v + u

tK@

3uv

k

Wiabdnty bg kirbpakmi wlnai gaynmj tlrbujl @D u

v

00K uvv

vK

3 00 uv


13/20

XL^TNDT


t@D

3 00 uv

k

Wiabdnty bg kirbpakmi wlnai gaynmj tlrbujl DF

v 3v uK

uv

vK

3 v u

tDF

3uv

k

Wiabdnty bg kirbpakmi wlnai gaynmj tlrbujl FK

u

v 00K uvv v

K3 00 uv

tFK

3 00 uv

k

Vbtka tnci 3 tK@

+ t@D

+ tDF

+ tFK

30000 uv

k

uv

k

uv

k

uv

k

3 00 uv

k0

00 uvv

7. PKNM XPB@AICNg rknm ns gkaanmj virtndkaay wntl k viabdnty Pv

kmf km b`sirvir ns cbvnmj lbrnzbmtkaay wntl viabdnty cv

, tli

viabdnty bg rknm riaktnvi tb b`sirvir wnaa `i ?

Pcv

3 Pv

cv

br vPc

3 0c

0P vv

kmf fnridtnbm3 tkm;

P

c

v

vwntl tli virtndka ks slbwm nm gnjuri.

vPc

vc

vP

Ixkcpai 0; Pknm ns gkaanmj virtndkaay kt spiif bg ;8 c/s kmf k ckm ns cbvnmj wntl viabdnty 7 c/s. Gnmf tli kmjai

kt wlndl tli ckm slbuaf lbaf lns uc`riaak tb kvbnf jittnmj wit.

Tbautnbm ?

v

rknm3 ;8 o v

ckm

3 7o

v

r.w.r.t. ckm3 ;8 o 7n

tkm 3;8

7 3 tkm;

9

4

Zlirins kmjai wntl virtndka


14/20

XL^TNDT


Ixkcpai 00 K ckm cbvnmj wntl 9c/s b`sirvis rknm gkaanmj virtndkaay kt tli rkti bg ;8 c/s. Gnmf tli spiif kmf

fnridtnbm bg tli rknm wntl rispidt tb jrbumf.

Tbautnbm ? vPC

3 ;8 c/s, vC

3 9 c/s

PCv

3 Pv

Cv

Pv

3 PCv

+ Cv

Pv

3 99

tkm 30

;, 3 tkm;

0

;.

Ixkcpai 04. K stkmfnmj ckm, b`sirvis rknm gkaanmj wntl viabdnty bg 08 c/s kt km kmjai bg 48 wntl tli virtndka.

(n) Gnmf tli viabdnty wntl wlndl tli ckm slbuaf cbvi sb tlkt rknm kppikrs tb gkaa virtndkaay tb lnc.

(nn) Mbw ng li gurtlir nmdriksis lns spiif, rknm kjknm kppikrs tb gkaa kt 48 wntl tli virtndka. Gnmf lnsmiw viabdnty.

Tbautnbm ? (n) cv

3 v n (ait)

Pv

3 ;8n ;84o

PCv

3 (;8 v)n ;84o

(;8 v) 3 8 (gbr virtndka gkaa, lbrnzbmtka dbcpbmimt cust `i zirb)br v 3 ;8 c/s Kms.

(nn)P

v

3 ;8n ;84o

cv

3 vx

n

PCv

3 (;8 vx)n ;84o

Kmjai wntl tli virtndka 3 48

tkm 48 34;8

v;8 x

v

x3 08 c/s

:. WIABDNV^ BG KXXPBKDL / TIXKPKVNBM NM VZB FNCIMTNBMNt ns tli dbcpbmimt bg riaktnvi viabdnty bg bmi pkrtndai w.r.t. kmbtlir, kabmj tli anmi obnmnmj tlic.

Ng tli sipkrktnbm ns fidriksnmj, wi sky nt ns viabdnty bg kpprbkdl kmf ng sipkrktnbm ns nmdriksnmj, tlim wi skynt ns viabdnty bg sipkrktnbm.

Ixkcpai 06. Xkrtndai K ns kt rist kmf pkrtndai @ ns cbvnmj wntl dbmstkmt viabdnty v ks slbwm nm tli fnkjrkc kt t 3

8. Gnmf tlinr viabdnty bg sipkrktnbm

K

@ v


15/20

XL^TNDT


Tbautnbm ? v@K

3 v@

vK

3 v

vsip

3 dbcpbmimt bg v@K

kabmj anmiK@ 3 vdbs

Ixkcpai 09. Vwb pkrtndais K kmf @ kri cbvnmj wntl dbmstkmt viabdntnis v;

kmf v0

. Kt t 38, v;

ckeis km kmjai;

wntl tli anmi obnmnmj K kmf @ kmf v0

ckeis km kmjai 0

wntl tli anmi obnmnmj K kmf @. Gnmf tlinr viabdnty

bg

kpprbkdl.

; 0v;

f

v0

K @

Tbautnbm ? Wiabdnty bg kpprbkdl ns riaktnvi viabdnty kabmj anmi K@v

KXX3 v

;dbs

;+ v

0dbs

0

Ixkcpai 07. Xkrtndais K kmf @ kri cbvnmj ks slbwm nm tli fnkjrkc kt t 3 8. Gnmf tlinr viabdnty bg sipkrktnbm

(n) kt t 3 8

(nn) kt t 3 ; sid.

6c

4c/s

6c/s

4c

K

@

Tbautnbm ? (n) tkm 3 4/6v

sip3 riaktnvi viabdnty kabmj anmiK@

3 4dbs + 6snm

3 4.9

6+ 6.

9

43

9

063 6.< c/s

6c

4c/s

4dbs

6dbs

4snm

6snm

6c/s

4c

K

@(nn) 3 69

vsip

3 riaktnvi viabdnty kabmj anmiK@

3 4dbs + 6snm

3 4.0

;+ 6.

0

;3

0

:c/s

:c

4c/s

4dbs

6dbs

4snm

6snm

6c/s

:c

K

@

3 69

:.; Dbmfntnbm gbr umngbrcay cbvnmj pkrtndais tb dbaanfiNg twb pkrtndais kri cbvnmj wntl umngbrc viabdntnis kmf tli riaktnvi viabdnty bg bmi pkrtndai w.r.t. btlir

pkrtndai ns fnridtif tbwkrfs ikdl btlir tlim tliy wnaa dbaanfi.

Ixkcpai 0:. Vwb pkrtndais K kmf @ kri cbvnmj wntl dbmstkmt viabdntnis v;

kmf v0

. Kt

t 3 8 , v;

ckeis km kmjai ;

wntl tli anmi obnmnmj K kmf @ kmf v0

ckeis

km kmjai0wntl tli anmi obnmnmj K kmf @. ; 0

v;

f

v0

K @(n) Gnmf tli dbmfntnbm gbr K kmf @ tb dbaanfi.

(nn) Gnmf tli tnci kgtir wlndl K kmf @ wnaa dbaanfi ng sipkrktnbm

`itwiim tlic ns f kt t 3 8

Tbautnbm ? (n) Gbr K kmf @ tb dbaanfi, tlinr riaktnvi viabdnty cust i fnridtif kabmj tli anmi obnmnmj tlic.

Vlirigbri tlinr riaktnvi viabdnty kabmj tli pirpimfnduakr tb tlns anmi cust `i zirb.

Vlus v;snm

;3 v

0snm

0.


16/20

XL^TNDT


(nn) vKXX

3 v;dbs

;+ v

0dbs

0

t 300;;kpp dbsvdbsv

f

v

f

:.0 Cnmncuc / Ckxncuc fnstkmdi ìtwiim twb pkrtndaisNg tli sipkrktnbm ìtwiim twb pkrtndais fidriksis kmf kgtir sbci tnci nt stkrts nmdriksnmj tlim tli

sipkrktnbm ìtwiim tlic wnaa ì cnmncuc kt tli nmstkmt, viabdnty bg kpprbkdl dlkmjis tb viabdnty bg

sipkrktnbm. (kt tlns nmstkmt vkpp3 8)

Cktlicktndkaay TK@

ns cnmncuc wlimft

fTK@3 8

Tncnakray gbr ckxncuc sipkrktnbm vsip

3 8.

Mbti ?

Ng tli nmntnka pbsntnbm bg twb pkrtndais kri ;r

kmf 0r

kmf tlinr viabdntnis kri ;v

kmf 0v

tlim slbrtist

fnstkmdi ìtwiim tli pkrtndais, fslbrtist

3|v|

|vr|

;0

;0;0

kmf tnci kgtir wlndl tlns sntuktnbm

wnaa bddur, t 3 0;0

;0;0

|v|v.r

Ixkcpai 0


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XL^TNDT

"ckmnsleuckrplysnds.nm" ;:

x 3 4:9 c

I@ 3 B@ BI 3 688 4:9 3 09 c@ut tli slbrtist fnstkmdi ns @G.

Grbc ckjmngnif gnjuri wi sii tlkt @G 3 I@ dbs 3 09 9

6

@G 3 08 c

Citlbf NN (Ysnmj tli dbmdipt bg ckxnck cnmnck)

K & @ ì kri tli nmntnka pbsntnbms kmf K,@ ì tli

gnmka pbsntnbms kgtir tnci t.@ ns cbvnmj wntl k spiif bg ;9 c/sid sb nt wnaa

trkvia k fnstkmdi bg @@ 3 ;9t furnmj tnci t.

K ns cbvnmj wntl k spiif bg 08 c/sid sb nt wnaa

trkvia k fnstkmdi bg KK 3 08t furnmj tnci t.

Tb

BK 3988 08 t

B@ 3 688 ;9 t

K@0 3 BK0 + B@0 3 (988 08t)0 + (688 ;9t)0 .....(n)Gbr K@ tb ì cnmncuc K@0 slbuaf kasb ì cnmncuc

ft

)'@'K(f 03

ft

)t08988()t;9688(f 00 3 8

3 0(688 ;9t) (;9) + 0(988 08t) (08) 3 8 3 ;088 + 69t 3 0888


18/20

XL^TNDT

"ckmnsleuckrplysnds.nm" ;

B

Dimtrbnf B. Kaa tli pkrtndais wnaa ciit kt tli dimtri. Dbmdimtrkti bm tli cbtnbm bg kmy bmi pkrtndai,

sky @.Kt kmy nmstkmt nts viabdnty ckeis kmjai 48 wntl @B. Vli dbcpbmimt bg tlns viabdnty kabmj @B

ns v dbs 48. Vlns dbcpbmimt ns tli rkti bg fidriksi bg tli fnstkmdi @B.

Nmntnkaay.

@B 348dbs

0/k3

4

k3 fnspakdicimt bg ikdl pkrtndai. Vlirigbri, tli tnci tkeim gbr @B tb `idbci

zirb

348dbsv

4/k3

4v4

k0

3

v4

k0.

Kantir ? Wiabdnty bg @ ns v kabmj @D. Vli viabdnty bg D ns kabmj DK. Nts dbcpbmimt kabmj @D ns v dbs 78 3 v/

0. Vlus, tli sipkrktnbm @D fidriksis kt tli rkti bg kpprbkdl viabdnty.

kpprbkdl viabdnty 3 v +0

v3

0

v4

Tnmdi, tli rkti bg kpprbkdl ns dbmstkmt, tli tnci tkeim nm rifudnmj

tli sipkrktnbm @D grbc k tb zirb ns

t 3v4

k0

0

v4

k

Ixkcpai 40. Tnx pkrtndais sntuktif kt tli dbrmirs bg k rijuakr lixkjbm bg snfi k cbvi kt k dbmstkmt spiif v. Ikdl

pkrtndai cknmtknms k fnridtnbm tbwkrfs tli pkrtndai kt tli mixt dbrmir. Dkaduakti tli tnci tli pkrtndais

wnaa tkei tb ciit ikdl btlir.


20/20

XL^TNDT

Tbautnbm ? Wkpp

3 W Wdbs 78 3 W W/0 3 W/0

k

k

k

kk

v vdbs78

v

78

k

t 3kppW

k3

0/W

k3

W

k0

Ixkcpai 44. K cbvis wntl dbmstkmt viabdnty u kabmj tli x kxns. @ kawkys lks viabdnty tbwkrfs K. Kgtir lbw

cudl tnci wnaa @ ciitK ng @ cbvis wntl dbmstkmt spiif v. Zlkt fnstkmdi wnaa `i trkviaaif `yK kmf @.

Tbautnbm ? Ait kt kmy nmstkmt tli viabdnty bg @ ckeis km kmjaiwntl tlkt bg x kxns kmf tli tnci tb dbaanfi ns V.v

kp p3 v u dbs

3V

8

kppv ft 3 ft)dbsuv(

V

8

............ (;)

Mbw iquktnmj tli fnspakdicimt bg K kmf @ kabmj x fnridtnbm wi jit

uV 3 ftdbsv ....... (0)Mbw grbc (;) kmf (0) wi jit

3 vV ftdbsu

V

8

3 vV V

8

ftdbsvv

u3 vV

v

u. uV

V 3 00 uv

v

Mbw fnstkmdi trkviaaif `y K kmf @

3 u 00 uv

v

kmf v 00 uv

v

3 00 uv

uv

km f00

0

uv

v

Date post:	03-Jun-2018
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Relative Motion Theory_E

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