The problem of the dog chasing the rabbit 10, the problem of the dog chasing the rabbit

<> assume that a hound's velocity is v1, starting from (l,0) (where l is the s given by the problem, v1 is v2 of the problem, and v0 is the v1 of the problem), and t time corresponds to the coordinates (x,y).

Since the rabbit and the hound set off at the same time when t=0, the rabbit coordinates are (0,v0*t).

The direction of the dog's velocity points to the rabbit, so the line between the dog and the rabbit is a tangent of the trajectory at (x,y) for any time t.

So it can be seen from the geometric relationship.

The red-painted section in the picture is the distance traveled by the hounds.

So, it is obtained by the curve length formula.

Cause. <>

n∈(1,+∞

It is obtained from the above three formulas.

Both sides are differentially obtained at the same time.

The above equation plus the initial conditions of x=l, y'=0 can solve the dog chasing rabbit curve. As for how to solve it, the landlord can think about it. Its trajectory equation is.

Let x=0, then y and t can be solved.

y0 is the ordinate of the rabbit when it finally catches up.

t is the catch-up time.

Draw a rough image, e.g. n=2, l=5

Of course, the above is the solution of high numbers, if the subject sees this problem in the physics competition book, it is recommended to use the physical understanding method.

Hope it helps, thank you!

The answer to S Upstairs (v2-v1) is correct.

If you don't understand, you can think of it like this:

Suppose it takes time t for the dog to catch up with the rabbit, then the distance traveled by the rabbit in time t is:

y=v1 * t, the distance the dog walks is y'=v2 * t and when the dog catches up with the rabbit, the difference in their distance is s, i.e. .

y'-y=s

v2*t-v1*t=s

t=s/(v2-v1)

Solution. Speed addition and subtraction is more abstract, you have to understand now, speed can also be added and subtracted, in the future when you encounter this kind of problem, you don't need the above analysis process, you can do the solution directly.

The simplest solution to the problem of hunting dogs chasing rabbits is to set up numbers. Set the unit time to get a few steps per second. Set the step size to find the respective speed. After the speed is obtained, the basic formula of catching up or encountering is used to solve the problem according to the problem.

Example of the problem of hunting dogs chasing rabbits:

The hunter went hunting with the hound, and the moment he found the rabbit (at this time, the hunter, the hound, and the rabbit were at the same point), the hunter hesitated for a moment before giving the order to let the hound chase him, and by this time the hale had already run 6 steps. It is known that the hound's gait is large, it runs a distance of 5 steps, and the rabbit runs 9 steps; But the rabbit moves fast, and the time it takes for the hound to run 2 steps, the rabbit can run 3 steps. then How many steps does a hound run to catch up with a rabbit?

The distance for a hound to run 5 steps (9 steps for a rabbit) is 1 meter, and the time for a hound to run 2 steps (3 steps for a rabbit) is 1 second.

S dog = 1 5 (m step), s rabbit = 1 9 (m step);

T dog = 1 2 (second step), t rabbit = 1 3 (second step);

v dog = 2 5 (m s), v rabbit = 1 3 (m s);

The distance that the rabbit runs in 6 steps: s=6*(1 9)=2 3 (m);

It takes the Hound to catch up with this distance: t=s (v dog-v rabbit) = 10 (seconds);

The number of steps that the hound runs in 10 seconds is: 10*2=20 (steps).

Gree and Thin Dogs can chase rabbits, and both breeds of dogs run faster than rabbits.

1. Thin dogs. The slender dog has an elongated body, an extremely elastic back, and a streamlined overall structure, making it very good at running. It is said that it can run at speeds of up to 60 kilometers per hour, and the "champion of sprinting" cheetah has a maximum speed of 90 kilometers per hour.

2. Gree dog.

With a speed of more than 60 kilometers per hour and a maximum of 70 kilometers per hour, the Gree Dog is the fastest dog in the world. It has an elegant temperament, a beautiful body structure, alertness and a lot of feelings. There are rules.

With a smooth gait when walking and swift as a flight when running, the Gree Dog can accurately hunt down small, sensitive animals. Since ancient times, hares have been competitors chased by Gree dogs.

Walking in the same direction: a dog can never catch up with a rabbit! The dog walks 5 steps and the rabbit can walk 9 steps, and when the dog walks 10 steps, the rabbit can walk 18 steps; And the distance that a dog walks 10 steps is equivalent to the distance that a rabbit walks 15 steps (because the distance between a dog and 2 steps is that of a rabbit and 3 steps).

15 steps 18 steps, so the longer you run, the farther the dog is thrown by the rabbit.

Walking in the opposite direction: When the dog walks 10 steps, the rabbit walks 18 steps, running the same distance as the rabbit 15 steps. The speed of the dog is 15 18 of the speed of the rabbit, which is 5 meters, that is, 9 and 1 11 meters.

So the dog can catch up with the rabbit in the 9 and 1 and 11 meters in the wild of Shenxuye.

To catch up, rural hounds often catch rabbits.

<> breeds of rabbit chasing dogs mainly include twig banquet dogs and Gree dogs, and the fine land fighting dogs belong to the Chinese pastoral dogs, including Shandong fine dogs, Inner Mongolia fine dogs and Shaanxi fine dogs. Gree dogs are known as the natural enemies of hares, and they can run at speeds of more than 64 kilometers per hour, making them the fastest dogs in the world.

1. You can get rid of dogs with speed, rabbits are more flexible, and finally you can use the surrounding environment.

2. In the rabbit family, the fastest breed is the snow hare. According to expert estimates, snow hare can run at speeds of up to 60 kilometers per hour. Therefore, even if you are spotted by a natural predator, you will be able to deal with it calmly, and with your flexible skills and extraordinary speed, you will have a high chance of escaping.

1. Hunting instinct and endurance: Graeber blindly takes the hound

Chasing rabbits in the field requires a dog with good hunting instinct and enough stamina, and the Graeber Spaniel is simply an excellent choice. This breed of dog is tall, has a unique hunting talent and a strong physique, and is perfectly suited to hunt rabbits in the open field.

However, it should be noted that the Graeber Hound has a high level of activity and requires a long period of exercise and proper training on this basis to achieve a better chase effect.

2. Sensitive speed and capture ability: Greyhound

The Greyhound is a sensitive, fast, and aggressive dog that can quickly catch rabbits and maximize their grasp of the opponent's pace, so as to catch up with them and force them into a desperate situation in a very short time. Due to the speed of this dog, it will quickly force the rabbit into a relatively enclosed area, making it easy to catch it.

However, it should be noted that the greyhound has a strong attack power, which means that the danger is relatively high. Proper training and control is also required to better perform the field rabbit chasing activity.

3. Agile and agile pursuit ability: Beagle

The Beagle is a short but extremely agile and agile dog. Has a strong hunting instinct and is able to hunt down rabbits with an excellent sense of smell on the ground. Due to their smaller size, beagles are better able to chase rabbits between hiding spots in the field.

However, it is important to note that beagles can be attacked by rabbits due to their size, and special care needs to be taken to protect the dog from harm when doing this activity.

4. Multi-purpose ability: universal hunting dog

The Universal Hound is a versatile dog that can adapt to different venues and environments. This dog has excellent hunting ability and a keen sense of smell, and can also be used for a variety of purposes such as hunting and conservation. For a rabbit chase on the grounds, the Universal Hound is a perfect choice.

However, it is important to note that universal hounds require proper training and guidance for each use in order to achieve the best results in the high-intensity sport of chasing rabbits in the field.