The problem in the rocket's equation is not in its derivation but in the final result. The force on the rocket is finally found to be F = mdv/dt = -v_edm/dt and as dv/dt = a the force is F = ma and not dp/dt.

Edited November 28, 20241 yr by martillo

Might help if you look at the time aspect imsteas of writing 

\[a=\frac{dv}{dt}\] 

Write 

\[a(t)=\frac{dv}{dt}\] 

Secondly momentum includes mass via \[p=m*v\]

So where is the issue ?

Others have tried explaining this to you in the older thread 

 

 

Edited November 28, 20241 yr by Mordred

I don't understand your point.

p = mv and dp/dt  = mdv/dt + vdm/dt what is different from mdv/dt = ma for variable mass systems like the rocket. The force on the rocket is found to be F =ma what is not dp/dt.

!

Moderator Note

You had a thread on this already. It was locked.  

Don’t be hijacking someone else’s thread to bring it up