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Hw-1,PARI TA T BANGR TEE
12--here escepe iSvelbcty) no
We can
-ESsepe velocty om Surfue is mihimm
tmosphe rit^ resistonce^ So^ he^ Sy^ ste^ is^ Con^ Servative^.
Psthpstetia^ ernegy
ivon: G= 6.67^ xmk's^ Re^ =^6371 kmy^ Me=^ 6x|o^ Ikg
Scme
ot sofce^ far^ bjeet^ mass(m)^ = -^ GMm
CM-So
Re
vebaty reguived^ for^ a^ par^ hele^ to
At r> o,o .'. At Y>,V2 0.
byet e^ to^ erh^ atany^ distomce^ Y>^ Re^ -^ aMm
-the-beAso, ponkcoorhcat^ r’e,^ le^ just^ the^ reches^ kEr.^ ()=^ O,it^ we^ neac^ he^ min.^ escepe^ velocity,
2GMRe
Re
2x6-67KID X 6xo4Re
6371 x1o3 =nl.^ || 2o8.52kms :.D^ ms trovee
Conservahan þriheiHe^ ener95^ T^ +V=^ T4V2.
(X,YYoCenter d Posim masses : Take (^) dtd to
2
I
=(acos &, asin o
2
X,=(acos8 coso, a sino tsind
V+V = 2&9+
2
2
TheCordncte se tuo aGngles this olescrbes 6 areall heposi hns 2 2 gene roleod vebaheo
2
Lot he centev he yod on he civele
2
and (^) let the (^) rod make (^) amg le a (^) win he
Ttal ke CT)^ =^ Lmvt^ +^ Lm^ =^ Jnlvv$).
+ acos +e cos t al caso cos o
whele the t sig tels abot bo macsey. Ohe has t, Sne has -.
4
2
4
2
(^2) al Sinb Sin o e d
( The^ t^ tevwms^ cemad^ ot^ ahen^ you^ add^ ) T6telCoor dnatey kinehc energy in hen
.8= k
eg:
M
dt
Sd
dfalt
mi
ShceCen petal The 7ce Sish amd sn )ehegràvt, RHs isSo ohhosite,e Sy stemn >Covldhereig be ain^ tateeab^ betueen
Let M mitmz CTstal mass)
dtL^ dtd
m,
Since he Lagrngian doent des end n tme explicty: 4:-L = Const =
dt dt
2d (^) ovder
Dg t
wheve k DDis a cnst
Enrgy Stem (E)
=dHdT
2
M
Since g =^ k
2
for fe atlng body
2
Genealeed cssvchte :
is nfdf.
2
ThisUSng isa (mstent^ The(snstont^ first Dtermim^ CE).he^ Sermol^ srder^ a:.^ esu^ obteihed
2
23 Far^ d'ssipetive^ foces^ :CvNf^ to)
2
2- m,
2
k
whee (^) Si is^ General:ed^ fce^ S=-SE
-V=
nomjevotive,
T= Lm (knehc Cnerg)
2
