How can the boatman cross the river in the shortest time?

[harini_5]

hi!
here is a problem for which I cannot really feel the answer though I know the answer
here it is
A boat can travel at a speed of 3m/s on still water.A boatman wants to croo a river whilst covering the SHORTEST POSSIBLE DISTANCE.in what direction should he row w.r.t the river bank if the speed of the water is 4 m/s
the solution to this problem was given in an orientation class and the main step is that the resultant velocity must be perpendicular to the velocity of man in still water
Plz explain me why is it so...
thanks in advance...

 

[LowlyPion]

hi!
here is a problem for which I cannot really feel the answer though I know the answer
here it is
A boat can travel at a speed of 3m/s on still water.A boatman wants to croo a river whilst covering the SHORTEST POSSIBLE DISTANCE.in what direction should he row w.r.t the river bank if the speed of the water is 4 m/s
the solution to this problem was given in an orientation class and the main step is that the resultant velocity must be perpendicular to the velocity of man in still water
Plz explain me why is it so...
thanks in advance...

In the frame of reference of the water, all he wants to do is row straight across to the other shore doesn't he? Because that it his shortest rowing distance. That will be his least effort.

 

[harini_5]

I'm sorry I cannot get it...

 

[ideasrule]

hi!
here is a problem for which I cannot really feel the answer though I know the answer
here it is
A boat can travel at a speed of 3m/s on still water.A boatman wants to croo a river whilst covering the SHORTEST POSSIBLE DISTANCE.in what direction should he row w.r.t the river bank if the speed of the water is 4 m/s
the solution to this problem was given in an orientation class and the main step is that the resultant velocity must be perpendicular to the velocity of man in still water
Plz explain me why is it so...
thanks in advance...

The answer given in your orientation class is wrong, because the shortest possible distance is the width of the river. For the boat to travel only the width of the river would require the man to pedal partially perpendicular to the river bank and partially against the water's flow.

If by "shortest possible distance" you mean "shortest possible time", then consider the situation from the water's perspective. The river bank is going backwards, the boat is in the water, and to cross the width of the river the man has to...