Test Your Intuition 35: What is the Limiting Distance?

(Just heard it today from Sergiu Hart.)

At time t=0, point A is at the origin (0,0) and point B is distance 1 appart at (0,1). A moves to the right (on the x-axis) with velocity 1  and B moves with velocity 1 towards A.  What will be the distance between A and B when t goes to infinity?

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