The problem of small boat crossing the river, the problem of small boat crossing the river and the t

Answer: If the end of the velocity vector is the center of the circle, and the vector size of the ship speed is the radius of the circle, then the tangent between the starting point and the circle is the direction of the velocity, and the extension line of the river bank is the shortest route.

The speed is the vector sum of the speed of the water and the speed of the ship, when the speed of the ship is less than the speed of the water, in the velocity vector triangle, the angle between the speed and the speed of the water is , and the width of the river is s, then the voyage is s sin. It can be seen that when a larger value is obtained, the range is smaller. In this problem, the magnitude and direction of the water velocity vector have been determined, and the magnitude of the ship velocity vector has been determined, and the direction has not been determined.

Therefore, when the speed of the ship is perpendicular to the speed of the ship (the velocity vector triangle is a right triangle), the maximum angle can be obtained, and the range will be the shortest. The answer to the question is based on this line of thinking.

When the speed of the boat is greater than the speed of the water, the speed of the boat can be deflected upstream, so that one of its sub-speed and the speed of the water can be canceled out, and the river can be crossed in a straight line.

However, when the speed of the ship is less than the speed of the water, this method cannot be chosen, and it can be seen that only when the direction of the V ship and the actual speed is perpendicular to the direction of the actual velocity, the angle between the actual speed and the V water is the largest, that is, the displacement is the shortest, and the conclusion can be obtained from the calculation.

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 velocity is , the boat can cross the river vertically when the boat is diagonally upstream in the direction of (-90), and the crossing time t=s cos(-90)v boat.

When the velocity of the current is greater than the speed of the ship, the combined velocity of the velocity and the speed of the ship cannot be perpendicular to the riverbank, you can also try to draw a diagram, but the premise is that the velocity is greater than the speed of the boat. But the boat has the shortest displacement, the practice is a bit complicated, we carefully understand, take the length of the ship's speed as the radius, and draw a circle with the position of the velocity arrow in the center of the circle, at this time there are countless tangents in the circle, and the tangent line of the initial position of the flow velocity should be found.

This tangent line coincides with the shortest displacement, and 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 formula to solve it. 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.

The formula for crossing the river in a physical boat, preferably with a diagram, is divided into 3 situations 1The speed of the boat in still water is greater than the speed of the current, perpendicular to the river bank.

The three cases of the problem of small boats crossing the river and their formulas are:1. The speed of the boat is all used to cross the river and not as a sub-velocity, so the shortest way to cross the river is to cross the river on the vertical bank, and the formula is t=s v boat.

2. When the speed of the ship is greater than the flow rate of the water, the combined velocity of the flow velocity and the speed of the ship can be perpendicular to the river bank, provided that the speed of the ship is greater than the flow speed. When the angle between the speed of the boat and the flow velocity is , the boat can cross the river vertically when the boat is diagonally upstream in the direction of (-90), and the crossing time t=s cos(-90)v boat.

Velocity physics terminology.

In the International System of Units, the dimension of velocity is lt (-1) and the basic unit is meters per second with the symbol m s. Maximum: vacuum speed of light c = 299 792 458 ms .

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, it is necessary 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 across the river, and the crossing time t=s cos(90)v boat.

3. The third case and formula.

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.

There are three situations in which a small boat crosses the blind imitation river, namely: crossing the river vertically, the boat tilting upstream to cross the river vertically when the speed of the boat is greater than the water speed, and the boat cannot cross the river vertically when the current speed is greater than the speed of the boat. In the first case, the boat crosses the river with the shortest time, and the formula is grinding t=s v boat.

In the second case, the boat can cross the river vertically, and the crossing time at this time can be expressed as t=s cos(-90)v boat. In the third case, the number of panicles of the ship shifts the shortest, and the formula is t=x vx=y vy, where vx=vo+(-vcx, vy=vcy, and vcx 2+vcy 2=vc 2

In the question of crossing a river by a small boat, the shortest time is to divide the width of the river by the speed of the boat.