The scene from the movie is [here](https://youtu.be/JAEnv1PvBvw)
I understand basic algebra and that’s about it.
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They launch from Florida. And to take advantage of the speed from the rotation of the Earth they launch straight east. That means that they will follow a great circle path, this looks like a sine wave centered on the equator when drawn up on a flat map. But while the earth rotates to the east the spacecraft orbit does not. So the orbit will appear to be moving west at about 1/24th of a rotation every hour. Using all this information you can draw a ground path of where the spacecraft will be each orbit. It will have to land along one of those ground paths.
The calculations shown and the explanation is pretty accurate as it is the type of calculations you would do to plan a mission such as this. Already before the cut she have calculated exactly how far before they reach the landing spot they need to fire the retro rockets. They were trying to figure out the mission parameters to figure out the launch window. There were no rendezvous on this mission so the window was pretty arbitrary but they still had to coordinate with the Navy and the weather forecasts. A skilled mathematician who had been working on these types of calculations and had the techniques and numbers in their head could easily do the rough calculations needed for these mission parameters in 5 minutes.
The coordinates are however wrong for the real mission. Bahamas is just too close to Florida. It takes about 90 minutes to orbit the Earth once, by which point the spacecraft would be east of Bahamas. And one orbit is too short to do all the measurements they wanted. So they went for three orbits. By which point Bahamas was already way off the ground track of the spacecraft. So they landed much further east, and even then landed further south to push the landing spot as far west as they safely could do. They ended up landing fairly close to the Dominican Republic, far away from Bahamas.
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