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A man wants to reach from \( A \) to the opposite corner of the square \( C \) (Figure). The sides of the square are \( 100 \mathrm{~m} \) each. A central square of \( 50 \mathrm{~m} \times 50 \mathrm{~m} \) is filled with sand.
\( \mathrm{P} \) Outside this square, he can walk at a speed \( 1 \mathrm{~m} \mathrm{~s}^{-1} \).
In the central square, he can walk only at a speed of \( v \mathrm{~m} \mathrm{~s}^{-1}(v1) \). What is smallest value of \( v \) for which he can reach faster via a straight path through the sand than any path in the square outside the sand?
(a) \( 0.18 \mathrm{~m} \mathrm{~s}^{-1} \)
(b) \( 0.81 \mathrm{~m} \mathrm{~s}^{-1} \)
(c) \( 0.5 \mathrm{~m} \mathrm{~s}^{-1} \)
(d) \( 0.95 \mathrm{~m} \mathrm{~s}^{-1} \)
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