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

In summary, the solution to the problem of finding the shortest distance for a boatman to cross a river with a speed of 3m/s on still water and a water speed of 4m/s is to row perpendicular to the velocity of the boat in still water. This was given in an orientation class, but it may not be the most efficient solution. If the goal is to minimize time instead of distance, then the man must pedal partially perpendicular to the river bank and partially against the water's flow.
  • #1
harini_5
36
0
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...
 
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  • #2


harini_5 said:
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.
 
  • #3


I'm sorry I cannot get it...
 
  • #4


harini_5 said:
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...
 

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

1. What factors affect the time it takes to cross a river?

The time it takes to cross a river can be affected by the width of the river, the strength and direction of the current, the depth of the water, and the terrain on either side of the river. Other factors such as weather conditions and the weight of the person or object crossing can also play a role.

2. How can I determine the shortest route to cross a river?

The shortest route to cross a river can be determined by analyzing the width and depth of the river, as well as the terrain on either side. In some cases, it may be necessary to scout the area or use a map or satellite imagery to identify potential paths. Additionally, considering the strength and direction of the current can also help determine the most efficient route.

3. Can I use a boat or other equipment to cross a river in the shortest time?

Yes, using a boat or other equipment such as a raft or kayak can be an effective way to cross a river in the shortest time. However, it is important to consider factors such as the availability and accessibility of these resources, as well as the experience and skill level required to use them safely.

4. What precautions should I take when attempting to cross a river in the shortest time?

When attempting to cross a river in the shortest time, it is important to prioritize safety and be aware of potential hazards. This may include wearing appropriate gear such as a life jacket, scouting the area for potential obstacles, and having a plan in case of emergency. It is also important to have the necessary skills and experience to navigate the river and any equipment being used.

5. Are there any techniques that can help me cross a river faster?

There are several techniques that can help you cross a river faster, such as using a diagonal crossing method to take advantage of the current, crossing in a group to distribute weight and provide assistance, and using equipment such as ropes or poles to aid in balance and stability. It is important to carefully consider the specific circumstances and choose the most appropriate technique for the situation.

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