A friend of mine offered me the following problem.
Suppose we have a rabbit and a fox in $\Bbb R^2$. The rabbit starts at time $t=0$ at the point $(0,0)$ and runs with constant speed $(1,0)$. The fox starts at the point $(0,h)$ aat time $t=0$ and runs with speed of absolute value $1$ towards the rabbit. We are to find the established distance between the fox and the rabbit (i.e. $\lim\limits_{t\to\infty}$).
I am aware that this problem can be solved via a good choice of variables and a careful analysis of the obtained differential equation. In case you're interested, I can post my solution.
I'd like to find a more physics-style solution (something along a finding a conservation law), any hints will be appreciated.
The answer (spoiler):
the answer is $h/2$.