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# Raindrops keep falling

13 replies to this topic

### #1 bonanova

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Posted 13 June 2012 - 09:56 PM

A while ago Bushindo posted a puzzle that asked whether
how wet you get moving a fixed distance in the rain
depends on whether you walk or run.

Let's assume there is a speed that keeps you the driest,
but you don't have the stamina for it. My question is what
speed should you run to get only twice as wet as optimal?

Assumptions you can make:
• You are [a rather squarish] 6 feet tall, 2 feet wide and 6 inches thick.
• You always move in a standing position, i.e you never lean.
• Shelter is 1000 feet away, on level ground.
• The rain is falling at a speed of 10 feet per second.
• At any given place or time there are 1000 raindrops per cubic foot.
Enjoy!
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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### #2 bushindo

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Posted 14 June 2012 - 02:19 AM

A while ago Bushindo posted a puzzle that asked whether
how wet you get moving a fixed distance in the rain
depends on whether you walk or run.

Let's assume there is a speed that keeps you the driest,
but you don't have the stamina for it. My question is what
speed should you run to get only twice as wet as optimal?

Assumptions you can make:

• You are [a rather squarish] 6 feet tall, 2 feet wide and 6 inches thick.
• You always move in a standing position, i.e you never lean.
• Shelter is 1000 feet away, on level ground.
• The rain is falling at a speed of 10 feet per second.
• At any given place or time there are 1000 raindrops per cubic foot.
Enjoy!

My take on this
Spoiler for approach

• 0

### #3 EventHorizon

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Posted 18 June 2012 - 10:27 AM

Spoiler for Agreement with Bushindo

Spoiler for Yay. Let's make this unnecessarily complicated!

Spoiler for Just out of curiosity...

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Posted 18 June 2012 - 02:24 PM

Wait a minute... before I even try to tackle this question...
There is actually a difference in the speed you walk vs how much wetter you will get?!

What is the best pace to get wet the least??????? SO CURIOUS!
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Posted 19 June 2012 - 05:16 AM

Think of this in terms of extremes.
If you go super fast, you will only get 1 block of rain hitting you.
If you stand still, you will get every block of rain hitting you (in that location).

Theoretically the faster you move, the less rain should hit you.

Now, you should get the same water contact on you whether standing still for one second, or running for one second. Standing still will be more water on top of you (head), while running will be making contact with your chest.
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Posted 19 June 2012 - 05:28 AM

I was too slow to edit, but here's why faster is better.

No matter how fast or slow you move, the front of your rectangle will ALWAYS hit a rectangle of water with the size of 6x2x1000.
It is impossible for you to not hit every water droplet in front of you (assuming equal and even distribution of water droplets).

Therefore the only discrepancy is how much water hits the top of your rectangle. The slower you go, the more hits your top.
So faster is better.
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### #7 bonanova

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Posted 19 June 2012 - 08:39 AM

Good analysis all, but it's actually faster than the answers given so far.

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Posted 19 June 2012 - 01:59 PM

Very interesting...
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Posted 19 June 2012 - 09:27 PM

Good analysis all, but it's actually faster than the answers given so far.

Well, your answer is based upon the assumption that the man can turn sideways while running.

If he is facing 'forward' the minimum raindrops is 12,000,000
If he can run while sideways, then the minimum would be 1,000,000

How did you get an optimal*2 of 3,000,000?
Should optimal *2 be either 2,000,000 or 24,000,000
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### #10 bonanova

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Posted 19 June 2012 - 10:18 PM

Well, your answer is based upon the assumption that the man can turn sideways while running.
I just tried it; it works.
Do you find that this is inconsistent with the OP?

If he is facing 'forward' the minimum raindrops is 12,000,000
If he can run while sideways, then the minimum would be 1,000,000
Fmin is 3, not 1. [6 feet x 6 inches]

How did you get an optimal*2 of 3,000,000?
I didn't. Dmin is 3,000,000 drops.

Should optimal *2 be either 2,000,000 or 24,000,000
See above.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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