From the story. Their teacher at Big Creek High School, Freida Riley, pushed the boys toward harder math and physics, and Newton's laws were the place to start. Every rocket, from a model to the Space Shuttle, runs on them. (More in October Sky.)
A rocket throws mass out its back. Pushing that exhaust down means the exhaust pushes the rocket up with an equal force: Newton's third law. That push is the thrust. It doesn't need air to push against, which is why rockets work in space.
Key idea
First law: with no net force, motion doesn't change. Second law: $F_\text{net} = ma$. Third law: forces come in equal, opposite pairs. At liftoff, up positive: $$\role[net force]{force}{F_\text{net}} = \role[thrust]{force}{T} - \role{mass}{m}\role[acceleration of gravity]{acceleration}{g}, \qquad \role{acceleration}{a} = \frac{\role[thrust]{force}{T} - \role{mass}{m}\role[acceleration of gravity]{acceleration}{g}}{\role{mass}{m}}.$$
Worked example: Liftoff
A $120\ \text{g}$ rocket has $6.0\ \text{N}$ of thrust. Find its acceleration.
- $m = 0.120\ \text{kg}$, so $mg = 1.18\ \text{N}$.
- $F_\text{net} = 6.0 - 1.18 = 4.82\ \text{N}$.
- $a = 4.82/0.120 \approx 40\ \text{m/s}^2$, about four times $g$.
Answer: $\approx 40\ \text{m/s}^2$
Common mistake
Using $a = T/m$. That gives $50\ \text{m/s}^2$ above, too big by $g$, because weight acts the whole time.