A Single Drop Of Rain

Suppose a single drop of rain falls from a cloud base of height of H km. That at an above-ground height of h metres, it has diameter d mm. It falls alongside a tall glass skyscraper. Suppose the rain-drop-to-skyscraper distance remains a constant k metres. Suppose the sun is upon the rain drop unobstructed, at angle a to the ground.

Consider the reflective properties of the the drop, the glass, and the human eye. Factor in the eneregies acting upon the rain drop. Consider other relevant factors and/or a few irrelevant ones.

Q1. How does the shape and width of the rain drop change over time?

Q2. From what locations and angles would the rain drop (or any reflection of it) be visible to the human eye?

Q3. What determines the temperature of a particular point within the rain drop? What is the formula?

Q4. Does the raindrop reach the ground?

Q5. At what height does it cease to be a rain drop?

Q6. What is altered by the raindrop’s mathematical/existential journey?

SAMPLE ANSWERS: The Fate of a Single Drop of Rain

A)

1. It stays mostly round, and gets smaller.
2. Locations of open eyes looking within the optical range of the observer’s eye, symetrical to the angle of the sun to the ground, and the glass building wrt to 2k
3. The sun. f(k,H,h,…) = g(f(k),f(H),f(h), f(…)) = 42
4. Yes.
5. 0 + d/2 – x; 0<x </x
6. Dirt.

B)

1. It vibrates and gets smaller.
2. Near windows.
3. The average temperature of neighbouring points. sum(temp(points))/sum(points);inclusive
4. No.
5. 6ft 8 inches.
6. An umbrella.

C)

1. It gets smaller over time t.
2. Anywhere where view of the rain drop is unobstructed.
3. Atomic theory. f(fhHkd) = shit happens!
4. No, the ground reaches it.
5. 0.
6. The ground and a little weed.