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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