Particle $$P_0$$ is at $$(0, 0)$$ and particle $$P_1$$ is at $$(0, 1)$$ at time $$t=0$$. $$P_0$$ moves right along the $$x$$-axis at speed $$1$$ and $$P_1$$ always moves directly towards $$P_0$$, also at speed $$1$$. In the long run, $$P_1$$ will be moving right along the $$x$$-axis at speed $$1$$, and so the distance between the two particles will no longer decrease. What is that final distance?

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