THE Rocket Equation

Tsiolkovsky rocket equation derivation.
To analyse the motion of a rocket we cannot apply Newton's 2nd Law directly and we need to consider conservation of momentum. We apply this to a rocket that is moving with an initial speed U and we use calculus to find its change in speed after some mass has been expelled from the rocket.
The epic first few seconds of footage are freely available from:

[zhelyo_physics]

This equation tells us that the speed of the rocket depends only the exhaust speed and essentially the fraction of the fuel mass/rocket mass! Pretty cool. To actually work out say, the acceleration of the rocket, we would need to consider the time derivative of the v, apply that to the fixed rocket mass, which should give us the thrust. Rocket science is cool!

[Mysoi]

Amazing!
This is why I love calculus.
Its powerful!
conservation law is also amazing!

[Rafid_Ahmed]

Thanks!! that was really clean, want more like this

[sanjeevambalam]

How did you suddenly make dm negative? In your equation above you assumed that delta m was positive when applying conservation of momentum, as you wrote that the rocket mass of m+delta m splits into two parts.

[JMU]

Very interesting equation ❤️ i needed that. Thank you 😊

[TW]

Hi, you probably get asked this a lot but what spec do you teach- I do OCR A?

[Mysoi]

I'm trying to derive a differential equation that completely determines the acceleration of the rocket, but I'm stuck. the change in velocity only depends on the initial and final mass. So, without knowledge of the mass rate of change or mass function, is it impossible to determine the acceleration, right?

[Mysoi]

Sorry I’m not quite get what Ve really is.
its the exhaust speed right, relative to the rocket or relative to the ground?

[sdasdfas]

Hello! Just out of interest what university did you go to?

[FiNLI]

is it weird that im a freshmen in highschool and im procrastinating doing geometry homework by learning how to do this

[aelinwhitehorn]

Shouldn’t the integral of 1/m be ln|m| as in the absolute value of m?