A Tale of Two Rockets

One of the main goals of a rocket is to speed up. The amount by which a rocket can increase its speed, after using up all its fuel, is called delta-vee.
Recall that the thrust of a rocket depends on two things: the amount of fuel used per second, and the speed with which the exhaust leaves the rocket:
```
                     dM
       thrust  =  - ---- * u
                     dt
```
There are many different ways to design a rocket; engineers may choose to emphasize one or the other of these terms, depending on their needs.
The F1 engine was used in the first stage of the giant Saturn V rocket in the Apollo missions. It was designed to create stupendous thrust by dumping lots of exhaust, quickly.
The ion engine aboard the Deep Space 1 spacecraft, on the other hand, uses its fuel very slowly -- but throws the exhaust out the back at a very high speed u.

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