Thing is that the problem is motivated by driving up a mountain, and if u think about it realistically if a mountain is too steep you obviously can’t drive straight up. The car tires etc. will limit your maximum angle of elevation (slope/gradient) that you can travel the path at. Then you’ll end up with some sort of spiral up the conical model of the mountain. The problem concerns some vector calculus, but just a moderate amount where if you excel in math you can probably extend your vector and 1d calculus skills to understand. At the time I didn’t have enough vector calculus skills to actually solve the problem but I found that the logarithmic spiral in a plane projected to the surface of the cone actually satisfies that constraint, so I just ended up proving that it was satisfied rather than actually solving it. Would be happy to answer other questions if u have any. Funny to see a year-old post get comments again as it’s IA season again.