Imagine that in a distant future, the robots become intelligent enough to be able to create spaceships and go and explore the universe. They are interested in understanding the universe but, more pratically, they also need to find resources in other planets to expand their colonies and improve their technology. So, they organize missions where they try to find new planets which can have metals or minerals of interest that they can extract. Suppose that during one of those missions a new potential planet is found and the scouts decide to land on the planet to better understand if there are relevant resources.

After the landing, the robots start to inspect a promising area but unfortunately one of them falls into a pit because the ground is not stable everywhere. Now, this scouting mission becomes a rescue mission.

The blue robot will use the Free Fall Formula and Polynomial Regression to save the yellow robot. A full explanation of the problem, the polynomial regression formulas and the results can be found in the video below from my official Youtube Channel.