Donovan Clump and Hermione Timmon are political candidates in the electoral race for "Most Thankless Job in Modern History".
Both candidates set out into the wilderness at the same time. Rains are pouring down, hence both candidates quickly get their feet wet. There are no winds of change, hence the rain is falling straight down at terminal velocity.
Ms. Timmon sets out walking in a straight line at a constant speed (significantly less than terminal velocity), consistent with her "go slow with what you know™" campaign slogan.
Mr. Clump, concerned about the rain's effect on his hair, tarries in the rain just outside the door for ten seconds, contemplating turning back. Ultimately he decides to run too. He takes off on the same straight path as Ms. Timmon, accelerating at a uniform rate and gaining campaign momentum, until catching up with Ms. Timmon ten seconds after he starts running.
All the while, the rains are falling at a constant rate.
Assuming the two candidates are identical in all respects except their differing motion paths (which one might consider their campaign trails), at the exact moment Mr. Clump catches up to Ms. Timmon, which candidate will have been pelted by the greater number of rain droplets?
In other words: which candidate is most washed up?
Modeling:
- assume both candidates are cuboids of identical dimensions ($2$ m tall by $\tfrac{3}{10}$ m side-to-side and front-to-back)
- all rain droplets hitting the candidates count, including their fronts
- all physical effects/considerations aside from the candidates' differing $v\left( t\right) \equiv \dot{x}\left( t\right)$ should be ignored
- Ms. Timmon's (constant) forward velocity is $0 < v_{\rm tim} < v_{\rm t}$, where $v_{\rm t}$ is the terminal velocity of a rain droplet
This is fundamentally a problem of constructing a very basic physical model, and then good old fashioned math.