# A drifting boat

A river is flowing at a uniform velocity of $$v = 10 \text{ m/s}$$. As shown in the diagram, $$P$$, $$Q$$, and $$R$$ are three points on a line perpendicular to the river such that $$PQ =QR = 100 \text{ m}$$.

A boat starts from point $$P$$ and moves at a constant speed of $$v = 10 \text{ m/s}$$ relative to the river. It moves in such a way that the direction of its resultant velocity is always perpendicular to the line joining the boat and point $$R$$.

If the boat drifts $$a$$ meters and takes $$b$$ seconds to land on point $$S,$$ submit your answer as $$a + b$$ to 3 decimal places.

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