A river is flowing from west to east at speed of 5 m/minute . A man on south bank of river, capable of swimming at 10 m/min in still water, wants to swim across river in shortest time. He should swim in direction a)due north. b)30 east of north. c) 30 north of west. d) 60 east of north. Justify you answer.

River = 5m/min V man = 10 m/minsuppose width of river is x mtsCase 1if he travels due norththen his resultant velocty ( due to velocity of downstream of water) acts 30 north of east and the distane to be covered to reach the other bank increses to = x/cos 30i.e., 2x /31/2 and resultant velocity is 11.2 m/minso time taken is x / 9.7 minsCase 2if he travels due 30 north of eastthen his resultant velocty ( due to velocity of downstream of water) actsdue north and the distane to be covered to reach the other bank will be x mts and resultant velocity is 8.7 m/minso time taken is x / 8.7 minsSo case 1 takes least timehe should travel due North(a)

Thanks and regards

 

Time taken to cross the river t = d/VsCosQ 
Foe time to be maximum 
CosQ = maximum 
Q = 0 degree 
So , summer should swim due north