In the space ,A rocket with mass
M moving with constant velocity of
V with no external force acting on it.
1) after sometime, the rocket release the fuel mass
M/2 in an instant to increase the velocity .the velocity of the fuel relative to the rocket =
V 1.1) using the law of conservation of momentum find the velocity of the rocket after the increase of the velocity
1.2) after the increase of the velocity , what is the sum of the kinetic energy of the fuel gas and the rocket?
2) (2nd situation . not the time after question 1) after sometimes the rocket release the fuel gas of mass
M/4 to increase velocity .after that the rocket realease another fuel gas of mass
M/4 to increase velocity. both of the velocity of the fuel relative to the rocket are
V.
2.3) after increases of the velocity 2 times what is the velocity of the rocket
2.4)the first time of release of fuel gas to increase the velocity of the rocket,what is the velocity of the fuel relative to the space
2.5)the second time of release of fuel gas to increase the velocity of the rocket,what is the velocity of the fuel relative to the space
2.6) after the increase of the velocity 2 times, what is the sum of the kinetic energy of the fuel gas and the rocket?
3) (3rd situation ) After sometimes the rocket release aa amount of fuel to increase it`s velocity.after that, it release the same amount of fuel as the first time to increase it`s velocity again.both of the velocity of the fuel relative to the rocket are
V.
3.7) after the second time of the release of the fuel,the velocity of rocket
kV ,find the value of
k (k is more than 1)
3.

from question 3.7, if the maximum amount of the fuel released is equal to
M ,what is the maximum value of
kplease help me solve it......very sorry for not able to type them in Thai...my notebook doesn't support Thai= =......thank you very much
if somehow the question seem confusing please ask me i might have mistranslated some of the details.....
thank you in advance