A man wants to reach from A to the opposite corner of square C ( shown in the figure) . The sides of the square are 100m.A central square of `50 mxx50m` is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he can walk only at a speed of v m/s (v>1). 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.