Boat crossing the river problem 15, how to solve the problem of small boat crossing the river

This is a physics question in the first year of high school, I am a student in Jiangsu, and I studied it in the first year of high school. This should be the "problem of small boats crossing the river", which is very basic.

Choose D. for this questionThe explanation is as follows: the boat moving to the opposite shore and the movement of the water can be regarded as two independent sub-movements, because the sub-motion is the same as the combined motion time, so the time for the ship to cross the river is equal to the time for the boat to cross the river vertically in still water.

Because the river width is certain and the speed of the boat is constant, the time does not change. Then, consider the total distance traveled by boat across the river. The total distance is the sum of the vectors of the two sub-distances, if the water becomes larger, and the time is the same, then one of the sub-distances becomes larger, and the other is the width of the river, which is constant, so, the total distance becomes larger.

I hope you will think about it carefully, or ask your teachers and classmates to wish you all the best in your studies.

d, according to the synthesis and decomposition of the movement. It is divided into upward and downward movements, the upward velocity is the speed of the boat, and the distance is fixed, so the time remains the same, but the speed of the movement to the right increases with the speed of the current. So the greater the velocity of the water flow.

The farther the distance (the sum of the squares of the top and right), but the time remains the same (the width of the river divided by the speed of the boat. ）

Pick D... Because the bow of the boat is always perpendicular to the river bank, the time to travel to the opposite bank is only related to the speed of the boat, not the speed of the current, but the current will shift the course of the boat, so the distance becomes longer, and it is the speed of the water that affects this distance.

d The velocity can be decomposed into vertical banks and parallel banks [water velocity] Because the vertical velocity is constant, the river width is constant, so the time is constant, but the greater the velocity of the water, the longer the horizontal displacement, so the longer the passage path.

The actual velocity of the boat (i.e., the combined velocity) is a result of the velocity of the vessel perpendicular to the river bank and the velocity of the water parallel to the river. The displacement of the boat perpendicular to the shore is related to the velocity of the ship perpendicular to the shore, and the displacement of the ship parallel to the river is related to the speed of the water, and the actual displacement of the ship is synthesized by the displacement in these two directions.

Because the width of the river is certain (i.e., the displacement of the boat perpendicular to the shore is constant) and the speed of the boat is constant, the crossing time is constant. If the velocity of the water flow is larger, the displacement parallel to the river is greater, so the actual displacement is greater, that is, the longer the distance.

In addition, if the bow of the ship is not perpendicular to the river bank, the speed of the ship should be decomposed into two directions, perpendicular to the bank and parallel to the river, and the latter should be combined with the current velocity to form a combined velocity parallel to the river direction.

d, it's too simple, you don't need to explain it, if you don't believe it, you can try it.

The three situations of the problem of small boats crossing the river and their formulas are introduced as follows.

1. The first case and formula.

First of all, to understand the meaning of the formula, to understand that the speed of the water when the boat crosses the river, has nothing to do with the time when the boat crosses the river, but only the speed of the boat. The speed of the boat is used to cross the river and not as a fractional velocity, so the shortest way to cross the river is to cross the river bank with the formula t=s v boat.

2. The second case and formula.

When the speed of the boat is greater than the speed of the water, the combined speed of the current speed and the speed of the ship can bend on the bank of the river, and you can also make a diagram to taste, but the premise is that the speed of the boat is greater than the speed of the flow. When the angle between the speed of the boat and the velocity of the current is , when the boat is inclined upstream with the target of (90), the boat can bend over the trapped river, and the crossing time t=s cos(90)v boat.

Three Feasts, Third Situations and Formulas.

When the speed of the flow is greater than the speed of the ship, the combined speed of the flow and the speed of the ship cannot bend on the riverbank, and everyone can also make a picture to taste, but the premise is that the speed of the flow is greater than the speed of the ship.

But the boat has the shortest displacement, the practice is a bit complicated, everyone carefully understands, to the length of the speed of the boat as the radius, to the flow of the arrow position of the center of the circle to draw a circle, at this time there are countless tangents on the circle, should find out the tangent of the initial position of the flow velocity, the tangent line coincides with the shortest displacement, the formula is s = river width v water v boat.

First of all, to understand the meaning of the formula, it is necessary to understand that the speed of the water when the boat crosses the river vertically has nothing to do with the time when the boat crosses the river, only the speed of the boat. The speed of the boat is all used to cross the river and not as a minute velocity, so the shortest way to cross the river is to cross the river on the vertical bank of the river, and the formula is t=s v boat.

When the speed of the boat is greater than the speed of the water, the combined speed of the current speed and the speed of the ship can be perpendicular to the river bank, and you can also try to draw it, but only if the speed of the boat is greater than the current speed. When the angle between the speed of the boat and the flow speed is , when the boat is obliquely upstream in the direction of (-90), the boat can cross the river vertically, and the crossing time t=s cos(-90)v boat.

When the current speed is greater than the speed of the boat, the combined velocity of the current speed and the speed of the ship cannot be perpendicular to the river bank. But the boat has the shortest displacement, the practice is a bit complicated, we carefully understand, to the length of the boat speed as the radius, to the velocity arrow position of the center of the circle to draw a circle, at this time there are countless tangents in the circle, should find out the tangent of the initial position of the flow velocity, this tangent line coincides with the shortest displacement, the formula is s = river width * v water v boat. Pay attention to the conditions given in the question, analyze it, and choose the appropriate Qingqi formula to answer.

Through the summary, it can be found that these three situations have their own conditions, which are clear at a glance, and the answers can be easily answered according to the ideas.

Categories: Entertainment & Leisure >> brain teasers.

Problem description: Three people and three Zen traces only wolves cross the river, both humans and wolves can row, there is only one boat on the river, each time the maximum number of scattered carries two things, on the same side of the bank if the number of wolves is greater than the number of people, people will be pushed down the river, both humans and wolves can not swim, how to cross the river?

Analysis: 1. A wolf passes alone, and people return.

2. Two wolves have passed, and one wolf has returned.

3. Two people have passed, one wolf and one person has returned.

4. Two people have passed, and one wolf has returned.

5. Two wolves passed, and one wolf returned.

6. The second flush pin wolf over.