On those cold, rainy days when you forget your rain jacket or umbrella and you want
to stay as dry as possible… should you walk and spend more time in the rain? Or should
you run, which means you'll be smashing into more raindrops from the side?
Assuming you haven't been fully soaked yet and you aren't jumping into puddles, the answer
is simple. As you move out of the way of one falling raindrop, you move into the way of
another. So the amount of rain hitting the top of you is constant, regardless of how
fast you're going. Alternatively, you can picture that the raindrops themselves are
stationary and you (and the earth beneath you) are moving upwards through the rain!
And since the volume of a parallelepiped (that's a 3D parallelogram) doesn't depend at all
on its slant, then no matter how fast you're moving horizontally the same amount of rain
will land on top of you each second.
Now, if you're not moving, the rain from the top is all you'll get. But if you ARE moving,
you'll also run into raindrops from the side and you'll get wetter. So in any given second,
you stay driest by standing still, and the faster you move the wetter you become.
But if you're trying to get from point A to point B, then standing still won't do you
much good. And en route from point A to point B, the total amount of rain you run into from
the side has nothing to do with how fast you're going - just like how a snowplow will plow
the same amount of snow from a stretch of road regardless of the exact speed it drives.
In the case of running through the rain, you can figure that out using parallelepipeds
So over a given period of time, the same amount of rain will hit you from the top, regardless
of how fast you're going. And over a given distance, you'll hit the same amount of rain
from the side - again, regardless of how fast you're going.
So your total wetness is equal to the wetness per second for rain from the top times the
amount of time you spend in the rain, plus the wetness per meter for rain from the side
times the number of meters you travel.
So to stay driest getting from one point to another, you should try to minimize the amount
of water falling onto you from above. And quite simply, that means getting out of the
rain as fast as possible.