The last example demonstrates the principle in rocket propulsion
only in rocket there a continuous stream of exhaust is ejected
with a velocity 
with respect to the rocket for the purpose
of changing the linear momentum of the rocket. If we consider for simplicity the case where no external forces acts then the total
linear momentum is conserved and hence
The first term is the momentum carried off by the exhaust with mass
moving with velocity 
with respect to
the rocket, the second term is the increase in momentum of the
rocket. (see the book for a proper derivation though you should note that there is confusion about the sign of 
. From Eq. 8-65 and on is a negative quantity). Dividing Eq. 11
by 
and going to the limit we obtain the ``rocket equation''
We can immediately integrate the equation to get
Remember we derived this equation assuming no external force
was acting on the rocket.
Obviously if the rocket is working against gravity or another
force which we could denote 
we should
modify the equation to read
We see that the speed of the rocket is controlled by the exhaust speed and the ratio of initial mass to final mass. This should help you understand why it is so important for rockets to shed unnecessary parts as they become so: For a given exhaust speed the only way to increase rocket speed is to increase the ratio of initial to final mass.
To illustrate that this actually works we have two little experiments. One we will do in class, the other we will do in front of the building on your way out.
Rather than a solid booster rocket I have a fire-extinguisher whose purpose is to expel momentum in the opposite direction to the desired direction of propulsion. We have a volunteer let her/himself be propelled forward by the fire-extinguisher.
When observing this phenomenon it is tempting to be left with the impression that it is the exhaust pushing against the atmosphere which is the source of the driving force. This is not true. Once the exhaust, in this case carbon dioxide has left the container it no longer interacts with the fire-extinguisher and cart. It is only through the very act of removing linear momentum from the systems that a balancing linear momentum is gained in the forward direction.