(adsbygoogle = window.adsbygoogle || []).push({}); a problem regarding momentum(from an entrance exam to Uni in Japan)(editted)

1. The problem statement, all variables and given/known data

2. Relevant equations

In the space ,A rocket with massMmoving with constant velocity ofVwith no external force acting on it.

1) after sometime, the rocket release the fuel massM/2in 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 massM/4to increase velocity .after that the rocket realease another fuel gas of massM/4to increase velocity. both of the velocity of the fuel relative to the rocket areV.

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 areV.

3.7) after the second time of the release of the fuel,the velocity of rocketkV,find the value ofk(k is more than 1)

3.8) from question 3.7, if the maximum amount of the fuel released is equal toM,what is the maximum value ofk

3. The attempt at a solution

this is what i thought of using this formulae

mv = − dm (−u +v + dv ) + (m + dm )(v + dv )

and i got the answer for 1.1 = 3/2M

is it correct?

for 1.2) should sum of the kinetic enegy equal to 2(1/2)(M/2)(3V/2)^2 ?

2.3) using the same formulae as 1.1 i got 5/4V and 1/5/6V

2.4,2.5,2.6,2.7 dun understand the concept= =

2.8) is it 0? because the mass of the rocket would also be reduced to 0?

sorry for not adding my own attempt at first I am new to this forum and hadnt yet to read the rule then

please ,your help will be greatly appreciated...

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this is the question in the entrance exam to a University in Japan.....so if the question seem confusing please do ask me....i might have mistranslated somethings.....thank you very much for helps

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# Homework Help: A problem regarding momentum(from an entrance exam to Uni in Japan)

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