Plane on a Plane

The URL of the third '???' post was indeed blog-post-19.html. Science, bitches!

Last week's question was: why do men like women with long blond hair, blue eyes, and large breasts?

I've actually known the answer for a while now, but for some reason it came to my mind recently. No, it's not because I met a large breasted women with long blond hair and blue eyes...

I first heard about this from (to my eternal shame) Psychology Today. In their article on 2007-09-20, they mentioned that there are evolutionary reasons behind these attractions. Specifically

• Hair is a good indicator of health. Since hair grows slowly, long hair shows health over a long period. It's lustrousness shows nutrition in a healthy body. Finally, blonde hair tends to turn brunette over age, and so it's also an indicator of youth.
• Blue eyes make the pupils easier to see, and hence easier to notice the dilation when the female is interested or aroused.
• Large breasts... I had apparently skipped over this one when I first read it. There are two theories: One is that it is an indication of fertility (but not the ability to lactate). The other is that large breasts sag more with age, and is therefore an indicator of youth.

It would be interesting to see if these hold true over people/populations who have no contact with at least the first two (the last one being hard to control). For example, if photos of women with long blonde hair only, with blue eyes only, with both, and with neither were shown to, say, men from a small village in China, would they rank their appearance in the same way?

For interested readers, the article I'm refering to is here.

This week's question is something I've wanted to solve for a while, but never got around to it. Might as well make this blog force me.

When you look up at a passing plane, usually you'll miss where it is at first glance. This is because the plane is high enough that there is some delay between the image of the plane and the sound of the plane reaching you. From this simple fact, it should be possible to calculate how quickly the plane is flying, as well as how far the plane is from you. The solution should be symbolic, and/but you can assume that:

• The speed of light is c_light = 299 792 458 m / s
• The speed of sound is c_sound = 340.29 m / s
• The plane is of length l. Assume you can recognize the model of the plane, and therefore know l.
• In the direction of light and sound, the plane is equidistant, d, from you. That is, at any moment the point of origin of light (which you see), the point of origin of sound (which you hear), and where you are standing are on a plane and forms an isosceles triangle.
• The plane flew in a straight line since it produced the sound until where you're looking at it now. The distance between those two points is kl, where k is any real number.
• The path of light and sound are separated by an angle θ (theta) as perceived at your location.

For bonus points: is it possible to calculate the same data if the plane was not equidistant from you, but flying in an arbitrary straight line? How/What other data is necessary?