Impulse dP = d(m + M)v = -dm v + (m + M) dv = F dT; so that F = -dm/dT v + (m + M) dv/dT showing that for every force there is an equal but opposite counter force so the net force, the thrust from the nozzle, is F = -dm/dT v + (m + M) dv/dT. -dmdT is the loss (minus sign) of fuel mass over time.
Note that F + dm/dT v = (m + M) dv/dT = (m + M) a where a is the acceleration of the rocket mass M and current on board fuel mass. Note that spewing the fuel mass out the nozzle contributes to the thrust F formed by the exhausts gases. Also note that F + dm/dT v - (m + M) dv/dT = 0 showing that the sum of forces SUM(f) = 0 indicating there are equal but opposite forces throughout the rocket's burn time. And that's Newt's Third. QED.
Note that F + dm/dT v = (m + M) dv/dT = (m + M) a where a is the acceleration of the rocket mass M and current on board fuel mass. Note that spewing the fuel mass out the nozzle contributes to the thrust F formed by the exhausts gases. Also note that F + dm/dT v - (m + M) dv/dT = 0 showing that the sum of forces SUM(f) = 0 indicating there are equal but opposite forces throughout the rocket's burn time. And that's Newt's Third. QED.
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3rd law of motion stated that for every action there is an equal and opposite reaction so when the rocket is launch it push off so the rocket can go up. The action is the exhaust pushing down and the reaction is the rockets going up