Flaneur in the rain - ii

Classical Mechanics Level 4

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 $\text{80 m}$ away.

The only problem is: it's pouring rain!

If you run across between the cafes at speed $v_0=\text{3 m/s}$ , how much water (in grams) do you absorb?

Assumptions

Approximate yourself as a shape with a vertical cross section of $A_\text{head}= \text{0.3 m}^2$ , and horizontal cross section $A_\text{body} = \text{1 m}^2$ .
The density of the rain in the air $\rho_\text{rain} = 0.8\text{ g/m}^3$
The rain falls at terminal velocity $v_\text{rain} = \text{9 m/s}$
All the rain that hits your body is absorbed.

The answer is 121.6.

1 solution

Beakal Tiliksew
May 24, 2014

The total amount of rain that soaks you(since it is homogenous) comes from the top as well as the side. The volume of water that that is hits you from the top is independent of whether you are standing still or moving, because when you move even though you missed the coming raindrop, you get in the line of the next raindrop.

${ w }_{ top }=\rho { A }_{ head }{ v }_{ rain }t\longrightarrow t=\frac { d }{ { v }_{ 0 } }$ $\quad \quad\quad\quad \quad \quad \quad\quad\quad \quad \quad \quad\quad\quad\quad=57.6$

And from the side

Let ${ w }_{ side }$ be the amount of water hitting you from the side,

${ w }_{ side }=\rho { A }_{ body }l\\ \quad \quad \quad =64g$

${ w }_{ tot }={ w }_{ top }+{ w }_{ side }$

@josh silverman , could u explain the answer for the first question of this set? and how was france?

Beakal Tiliksew - 7 years ago

Hey @Beakal Tiliksew , I just posted an argument for the first question. I wasn't there for very long, but Paris was a lot of fun. Between the parks, the subway, the museums, and all you see walking around, I was constantly thinking about things. I happened upon a road named for Fresnel (of the Fresnel lens), went to a science museum that is inside of a palace, and realized after two days that I wasn't telling people "I don't speak much French" but, instead, "I don't believe you really speak French".

Josh Silverman Staff - 7 years ago

i used the same equations,

wtop = .8x.1x9x80/3=19.2

wside = .8x.3x80 =19.2 right?

so total is 19.2+19.2 = 38.4

did i do something wrong?

Balagopal Indiradevi - 7 years ago

Nice solution!

Mardokay Mosazghi - 7 years ago

goodness i got the 2nd half.... :P :(

Birendra Korni - 7 years ago

i used the same equations, wtop = .8x.1x9x80/3=19.2 wside = .8x.3x80 =19.2 right? so total is 19.2+19.2 = 38.4 did i do something wrong?

Balagopal Indiradevi - 7 years ago

You have switched the value of $A_{head}$ and $A_{body}$

Beakal Tiliksew - 7 years ago

thankyou.... and sorry....

Balagopal Indiradevi - 7 years ago

@Balagopal Indiradevi – Oh, don't say that, I am happy to help.

Beakal Tiliksew - 7 years ago

Flaneur in the rain - ii

The answer is 121.6.

1 solution

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