Flaneur in the rain - iii

Suppose you're sauntering about Saint-Germain, Paris, from one cafe to the next, staying only as long as it takes you to knock down a few Brilliant problems. You're wrapping up at Brasserie Lipp and want to go to Cafè de Flore, which is across the street.

The only problem is: it's pouring rain!

If you want to absorb as little water as possible, how quickly should you run across the road?

Assumptions

  • Approximate yourself as a shape with a vertical cross section of AheadA_\text{head}, and horizontal cross section AbodyA_\text{body} .
  • The rain falls straight down at terminal velocity vrainv_\text{rain}
  • All the rain that hits your body is absorbed.
  • The width of the road is dd.
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