 16
 0
Main Question or Discussion Point
I found this problem in the book Resnick and Halliday many years ago (1992) and I had it in my mind until 2005 or so when I was able to get some advance.
"If you want to walk through a distance L in a rainy day, in order to get wet the little as possible what would you do, run as fast as possible, walk slowly or some intermediate velocity?"
I knew that the answer would be run as fast as possible because with an infinity velocity the drops of water would be static and that would be the least amount of water that you would find through your path, but how to prove it, and maybe that was not the right answer.
So I tried to solve the problem counting the number of drops that would collide with a box of dimensions A, B, C (height, length and width) during its path trough a L distance during a "uniform" rain. By uniform I mean the velocity of the drops is constant and equal for every drop, the drops are separated the same distance from each other, and the rain falls at an angle the same for every stream. Check the figure.
After much struggle I came to a formula that I don't have right now (sorry ) but I think the problem is very interesting and I was able to prove that the best velocity is as fast as possible, although it depends on the geometry of the object!!! that was something I was not expecting, so if the geometry of the body is appropiate the best possible it could be an intermediate value (something between zero and infinite).
I am going to check my papers to post the formula and main steps, and again I would like to share my results check if they are correct and get some feedback from the community.
"If you want to walk through a distance L in a rainy day, in order to get wet the little as possible what would you do, run as fast as possible, walk slowly or some intermediate velocity?"
I knew that the answer would be run as fast as possible because with an infinity velocity the drops of water would be static and that would be the least amount of water that you would find through your path, but how to prove it, and maybe that was not the right answer.
So I tried to solve the problem counting the number of drops that would collide with a box of dimensions A, B, C (height, length and width) during its path trough a L distance during a "uniform" rain. By uniform I mean the velocity of the drops is constant and equal for every drop, the drops are separated the same distance from each other, and the rain falls at an angle the same for every stream. Check the figure.
After much struggle I came to a formula that I don't have right now (sorry ) but I think the problem is very interesting and I was able to prove that the best velocity is as fast as possible, although it depends on the geometry of the object!!! that was something I was not expecting, so if the geometry of the body is appropiate the best possible it could be an intermediate value (something between zero and infinite).
I am going to check my papers to post the formula and main steps, and again I would like to share my results check if they are correct and get some feedback from the community.
Attachments

11.8 KB Views: 302