Sarthaks Test
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A man wants to reach from A to the opposite corner of the square C (Fig. 4.10). The sides of the square are 100 m. A central square of 50m × 50m 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?

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Consider the straight line path APQC through the sand. Time taken to go from A to C via this path

Tsand = (AP + QC)/1 + PQ/v

= (25√2 + 25√2)/1 + (50√2)/v

The shortest path outside the sand will be ARC.

Time taken to go from A to C via this path

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