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Re:A Physicist Reveals Why You Should Run in the Rain by heisenzombie on Tuesday October 22, 2024 @05:55PM (#41919124)
This is integrating over a distance, not a time. If you stay stationary you never get to your destination and get an infinite amount of rain (and the question is just ill posed).

If you move with even a tiny forward velocity then you'll start getting a few raindrops on your front. As you go faster, you get more rain per second on your front but spend less time in the rain.

Re:A Physicist Reveals Why You Should Run in the Rain by photon_rancher on Tuesday October 22, 2024 @10:38PM (#41921220)
Likewise the minimum amount of rain you could catch would only be on your front from moving at an infinite speed. You’d leave behind a tunnel of missing raindrops in the shape of your profile along your path.

As you move slower or faster you approach one limit or the other.