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find kinetic energy of rocket
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Asked by ashutosharnold1998 | 21 Jan, 2020, 12:47: AM
answered-by-expert Expert Answer
Mechanical energy of satellite on Earth surface,  MEe = (1/2)Mu2 - ( G Me M )/R  .............................(1)
 
After ejecting a rocket of mass (M/10), Mechanical energy MEO of satellite in an orbit of radius 2R is given by
 
MEO = - [ G Me (9/10)M ] / [ 2(2R) ]   = -(9/40) ( G Me M )/R  ......................(2)
 
Potential energy PE of ejected rocket is given by,  PE = - [ G Me (1/10)M ] / (2R) = -(1/20) ( G Me M )/R  .....................(3)
 
Hence kinetic energy KE of Rocket,   KE = MEe - MEO - PE .........................(4)
 
Using eqn.(1), eqn.(2) and eqn.(3), we get,   KE = (1/2)Mu2 - ( G Me M )/R + (9/40) ( G Me M )/R  + (1/20) ( G Me M )/R
 
Kinetic energy of rocket,  KE = M { (u2 / 2 )  -  [ ( 21 G Me ) / (40R) ] }
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