This new paper[1] considers this old problem once again. It considers the rain coming down vertically and at an angle, and also considers the geometry of a person (being approximated by a cylinder).

Abstract:

*The question whether to walk slowly or to run when it starts raining in order to stay as dry as possible has been considered for many years—and with different results, depending on the assumptions made and the mathematical descriptions for the situation. Because of the practical meaning for real life and the inconsistent results depending on the chosen parameters, this problem is well suited to undergraduate students learning to decide which parameters are important and choosing reasonable values to describe a physical problem. Dealing with physical parameters is still useful at university level, as students do not always recognize the connection between pure numbers and their qualitative and quantitative influence on a physical problem. This paper presents an intuitive approach which offers the additional advantage of being more detailed, allowing for more parameters to be tested than the simple models proposed in most other publications.*

It is a fun problem to play around in your head, especially when there can be a counter-intuitive answer.

Zz.

[1] A. Ehrmann and T. Blachowicz, Eur. J. Phys. v.32, p.355 (2011).

## 2 comments:

well, wouldn't the time outside affect the level of wetness? You would be outside for less time if you run than if you walk, right?

funnily enough i was working on this issue on my puzzles page.

my approach was to look at the problem in the limit. which to me seems like a sensible approach though i've not seen it done before. feel free to disagree.

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