Question

7. 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 1 = 38 cm, 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 v = 0.5 cm/s and down a wire segment at speed 2u, in what minimum time can the ant cross the groove with the help of this bridge?​

Answer 1

Answer:

Explanation:

From the diagram, we can determine that,

x=20cm

l=38cm

V=0.5cm

Minimum time,

⇒t=l2v+4r2−l2−−−−−−√v

⇒t=38×102×0.5+4(20)2−(38)2−−−−−−−−−−−√0.5

⇒t=38+4×400−1440−−−−−−−−−−−−√0.5

⇒t=38+1600−1440−−−−−−−−−−√0.5

⇒t=38+160−−−√0.5

⇒t=38+12.640.5

⇒t=38+25.29=63.29 sec

Therefore, the correct answer is 63.29 sec.