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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

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

Grade:11

2 Answers

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

Arun (askIITians forum expert)

Anish
105 Points
one month ago

To reach the opposite bank of the river in minimum time, the swimmer should swim at right angles to the direction of flow of river. He should swim in a direction due north

Let the width of the river be d. If the man swims at an angle θ with the direction of flow of water, his velocity component perpendicular to the direction of flow of water is 10sinθ
Time taken to reach the opposite bank: t=10sinθd
 t will be minimum when sinθ is maximum i.e θ=90

 

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