During the launch of a rocket into space, the exhaust gases from the engine possess momentum. Outline, with the help of an equation, how this causes the rocket to be propelled upwards.
Can someone point me in the right direction? I understand how the exhaust gases are used to propel the rocket upwards, and based on the specific mention of "momentum" I would think that $p=mv$ is to be referenced, but I don't understand how to link this to the question.
Answer
It does follow from the conservation of momentum. Consider the diagram (from Wikipedia) of a rocket expelling gas of mass $\Delta m$:
At $t=0$, the initial momentum is $$ p(t=0)=\left(m+\Delta m\right)V\tag{1} $$ but at $t=\Delta t$, we've lost some mass and gained some velocity, $$ p(t=\Delta t)=m\left(V+\Delta V\right)+\Delta m \left(V-v_e\right) \tag{2} $$ where $V_e=V-v_e$ with the difference coming from reference frames (see the above linked Wikipedia page). So now we have the momentum before & after the exhaust velocity, which shows an increase in the velocity of the rocket. The implication of this equation can be found in the post Why are rockets so big?
For other aspects of this problem (momentum conservation in the rocket equation), see
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