Flaneur in the rain - iv

Classical Mechanics Level 3

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 80 m \text{80 m} away.

The only problem is: it's pouring rain!

Suppose now that your hat and your coat absorb water with different efficiencies ϵ head \epsilon_\text{head} , and ϵ body \epsilon_\text{body} . How should you change your running speed in order to absorb as little water as possible?

Compare ϵ head v rain \epsilon_\text{head}v_\text{rain} , and ϵ body v 0 \epsilon_\text{body}v_0 to decide Compare ϵ head / v rain \epsilon_\text{head}/v_\text{rain} , and ϵ body / v 0 \epsilon_\text{body}/v_0 to decide No change in strategy You should run with speed ϵ body v 0 / ϵ head \epsilon_\text{body}v_0/\epsilon_\text{head}

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Josh Silverman by Josh Silverman

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1 solution

As the amount of water absorbed by the body is not dependent on the velocity of the runner, ϵ body \epsilon{}_\text{body} is not relevant. ϵ head \epsilon{}_\text{head} only changes how much water is absorbed, but still, the faster the character runs, less water will hit him. Therefore, the strategy stays the same: run as fast as you can. (Or just buy an umbrella, for Christ’s sake.)

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