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 $l = 32 c m,$ 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 $υ = 0.5 c m / s$ and down a wire segment at speed $2 υ,$ 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.

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answer is 80.

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Detailed Solution

$\frac{l}{2 υ} + \frac{\sqrt{4 r^{2} - l^{2}}}{υ} = 80$

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