Separation at t=t=\infty

Tom and Jerry both have equal top running speeds and are initially at points AA and B,B, respectively, separated by a distance of dd.

They both spot each other and immediately start running at their top speeds. Jerry runs on a straight line perpendicular to the line ABAB and Tom runs in such a way that its velocity always points towards the current location of Jerry.

Let r(t)r(t) denote the distance between Tom and Jerry at time tt.

Find limtr(t)\displaystyle \lim_{t \to \infty} r(t).

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