little math problem October 2018

10202018, 08:05 PM
Post: #4




RE: little math problem October 2018
I'm sure this isn't optimal, but just to get started:
The greatest distance at which the rovers can see each other is D. The radius of the planet is R. The rovers can travel at a maximum speed V. Assumptions: the planet is a perfect sphere, no water, no hills. Visibility is the same everywhere. One rover stays put, the other starts searching. It searches in an expanding spiral, where each circuit is 2 * D from the last. I'm ignoring the details of the shape of that spiral near its ends. The rover covers an area of 2 * D * V per unit of time. The area of the planet is 4 * pi * R^2, so it takes a time (4 * pi * R^2) / (2 * D * V) to search the entire planet, and the expected search time is half that. 

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