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# A river is flowing from west to east at a speed of 5m/s . A man on the south bank of the river capable of swimming at 10m/s in still water wants to swim across the river in the shortest time . In which direction should he swim

Arun
25763 Points
3 years ago
Dear student

------------> V river = 5m/min

V man = 10 m/minsuppose width of river is x mts

Case 1

if he travels due north

then 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 30

i.e., 2x /31/2 and resultant velocity is 11.2 m/min

so time taken is x / 9.7 mins

Case 2

if he travels due 30 north of east

then 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/min

so time taken is x / 8.7 mins

So case 1 takes least time

he should travel due north.

Regards

Anish
105 Points
one month ago