Clue to Puzzle #33: Should I Walk or Run in the Rain

33. Assuming I want to stay dry. Should I walk or run in the rain?

diagram someonewalkingin the rain It's helpful to look at the rain that falls on us in two aspects. The rain that lands on our heads and the rain the hits us on the front as a result of us walking forward.

The question then becomes how do these two elements change as a result of our speed.

In the main answer I use a scientific technique of looking in the limit. That is to say it's hard trying to think at realistic speeds, how our model would change if we sped up from 10mph to 11mph. We'd be in the rain for 9.1% less time but the rain would be hitting is 10% faster on the front...

In the limit we consider the extreme ends of speed. In this case moving very slowly, almost stationary and really fast like 1000mph or the speed of light.

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