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[fantasy]

   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 k

please 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

[ปิยพงษ์ - Head Admin]

   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?

...

If the velocity of the fuel mass is relative to the rocket, then the velocity of the fuel mass relative to the inertial frame is . This will decrease the speed of the rocket. Please have a look at the direction of the ejected fuel mass again. Is it or ?

[fantasy]

Thank you very much for your reply ,  ปิยพงษ sensei......sensei = teacher....I supposed you are a teacher....excuse me if I`m wrong javascript:void(0);
Lips Sealed__
hmmm....if I translate it word by word ,the following sentence` the velocity of the fuel relative to the rocket are V`will actually be `the velocity of the fuel looking from the rear of the rocket is equal to V`will this make anything change?

I`m thai by the way ...but my notebook just doesnt have thai keyboard = =...so if anyone want to explain in thai, it`s fine by me.....
thank you very much again....

I actually have attempted some parts of  the question......
and here are the answers to some question done by me....but I really do not know if it`s correct....

1.1) 3V/2

1.2) 5/8 *MV²

2.3) 5V/4 and 1/5/6 * V

2.4 - 2.7 no clue

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

Thank you very much your help will be greatly appreciated:)

[ปิยพงษ์ - Head Admin]

1.
1.1 ถ้าเชื้อเพลิงถูกขับออกไปทางด้านหลังด้วยอัตราเร็ว เทียบกับจรวจ ความเร็วของเชื้อเพลิงเทียบกับกรอบเฉื่อยจะเป็น
กฎการคงตัวของโมเมนตัมจะให้
  ซึ่งให้ความเร็วจรวดเป็น

1.2 พลังงานจลน์หลังปล่อยเชื้อเพลิง =

2. เดาว่าเป็นสถานการณ์ใหม่ที่ไม่ต่อเนื่องจากข้อ 1

เชื้อเพลิงที่ออกมาครั้งแรกมวล มีความเร็วเทียบกับกรอบเฉื่อยเป็น เหมือนข้อ 1
กฎการคงตัวของโมเมนตัมจะให้
  ซึ่งให้ความเร็วจรวดเป็น

เชื้อเพลิงมวล ก้อนที่สองมีความเร็ว
กฎการคงตัวของโมเมนตัมจะให้
  ซึ่งให้ความเร็วจรวดเป็น

ได้ความเร็วแล้วคงหาพลังงานจลน์ต่อได้


ที่เหลืออ่านโจทย์ไม่ค่อยรู้เรื่อง 

[fantasy]

Thank you very much again.......

after after i read the question carefully and try to rephrase it again, 

2.4 and 2.5 is actually asking for the velocity of the fuel released from the rocket relative to the space each time
is it O for the first time and V/3 for the second time?

3)สถานการณ์ใหม่ที่ไม่ต่อเนื่องจากข้อ 1 and 2
it`s quite the same as question 2 because the amount of the fuel release each of the 2 times is the same but it`s not specified.
3.7 kV is the velocity of the rocket after releasing fuel for 2 times.....the question ask for the value for k given that it`s more than 1

[ปิยพงษ์ - Head Admin]

Thank you very much again.......

after after i read the question carefully and try to rephrase it again, 

2.4 and 2.5 is actually asking for the velocity of the fuel released from the rocket relative to the space each time
is it O for the first time and V/3 for the second time?

...

Yes, as shown above in my answer before using them to find the velocity of the rocket after each fuel ejection.