Rocket Thrust: Power Your Launch Into Space

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TL;DR
Confusion of thrust of a rocket
I saw the information of thrust of a rocket in the hyperphysics website, but I cant understand it.
1.why do the problem need to observe in two frame ( from an external framework and rocket frame of)?
2.why do the exhaust velocity relative to the rocket u=u+deltav-U?

Thank You
thrust of rocket2.png
 
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The reference frame of the rocket is the easiest one. You can always choose whatever reference frame you want but why make it harder than needed?
2.why do the exhaust velocity relative to the rocket u=u+deltav-U?
Where do you get that from? The exhaust velocity relative to the rocket is u which is not equal to u+deltav-U.
 
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mfb said:
The reference frame of the rocket is the easiest one. You can always choose whatever reference frame you want but why make it harder than needed?Where do you get that from? The exhaust velocity relative to the rocket is u which is not equal to u+deltav-U.
typo,why do the exhaust velocity relative to the rocket u=v+deltav-U? should be "v" not "u".
i get the information from this website: http://hyperphysics.phy-astr.gsu.edu/hbase/rocket.html#c1
thank u for your reply
 
The rocket speed after expelling the exhaust is v+delta v, the ejected material moves at U by definition. They just calculate the difference, which is v + delta v - U
 
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