A semi-cylindrical groove of radius r=20 cm is made on a horizontal floor. An ant wants to cross the groove. A boy decides to help the ant making a bridge consisting of straight wire segments. But all the wires available are of length $l=32cm,$ so the boy rigidly connects two wires at right angle and places the bridge in the groove as shown in the figure. If the ant can crawl up a wire segment at speed $\upsilon =0.5cm/s$ and down a wire segment at speed $2\upsilon ,$ in what time in seconds can the ant cross the groove with the help of this bridge?. The left part of the bridge is just inside the groove.