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Circular motion problems. From one point on the circular route

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« From point A circular track drove out» — 251 tasks found

Task B14 ()

(views: 605 , answers: 13 )

A cyclist left point A of the circular track, and 10 minutes later a motorcyclist followed him. 2 minutes after departure, he caught up with the cyclist for the first time, and 3 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 5 km. Give your answer in km/h.

Task B14 ()

(views: 624 , answers: 11 )

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 10 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 10 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 691 , answers: 11 )

A cyclist left point A of the circular track, and 10 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 15 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 10 km. Give your answer in km/h.

Answer: 60

Task B14 ()

(views: 612 , answers: 11 )

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 47 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 47 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 608 , answers: 9 )

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 19 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 19 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 618 , answers: 9 )

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 2 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 50 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 610 , answers: 9 )

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 26 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 39 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 622 , answers: 9 )

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 20 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 (

Unified State Exam-2014 Problem solving

Circular movement (closed track)

Faber Galina Nikolaevna –

mathematics teacher of the highest category

KMOU "Gymnasium named after Gorky A.M."

Moskalensky municipal district Omsk region

v 2 respectively), then the 1st cyclist approaches 2 at a speed v 1 – v 2.

the first time he catches up with the 2nd, he covers the distance one lap more. Show At the moment when the 1st cyclist catches up with the 2nd cyclist for the second time, he covers a distance of two laps more, etc. Continue" width="640"

If two cyclists simultaneously start moving around a circle in one direction with speeds v 1 and v 2 respectively

At the moment when the 1st cyclist

for the first time catches up with the 2nd,

he travels a distance

one circle more.

Show

At the moment when the 1st

cyclist in

catches up for the second time

2nd, he passes

two distance

more circle, etc.

Continue

1. From one point on a circular track, the length of which is 15 km, two cars started simultaneously in the same direction. The speed of the first car is 60 km/h, the speed of the second is 80 km/h. How many minutes will pass from the start before the first car is exactly 1 lap ahead of the second? ,

15 km less (1 lap)

1 red

2 green

The equation:

The slide shows an algebraic solution. Although the problem can be solved using an arithmetic method.

1) 80 – 60 = 20 (km/h) chasing speed. At this speed, the 2nd car must cover a distance of 1 lap (15 km).

2) 15:20 = 3/4 (h) = 45 (min).

x we get in hours.

one circle more.

Don't forget to convert to minutes.

2. From one point on a circular track, the length of which is 10 km, two cars started simultaneously in the same direction.

The speed of the first car is 90 km/h

1 car

10 km more (1 lap)

2 green

2 cars

1) 90*(2/3) = 60 (km) the first car traveled in 40 minutes. This is 1 lap more than the distance covered by the second car.

2) 60 – 10 = 50 (km) the second car traveled in 40 minutes.

3) 50: (2/3) = 75 (km/h)

Answer: The speed of the second car is 75 km/h.

one circle more.

v 2 respectively), then the 1st cyclist approaches 2 at a speed v 1 – v 2. At the moment when the 1st cyclist catches up with the 2nd for the first time, he covers a distance of half a circle greater than 7: 21 = 1/3 (h) Show. 4" width="640"

If two cyclists simultaneously start moving in a circle from two diametrically opposite points of a circular track with speeds v 1 and v 2 respectively

(v 1 v 2 respectively), then the 1st cyclist approaches 2 at a speed v 1 – v 2.

If two cyclists simultaneously start moving around a circle in one direction with speeds v 1 and v 2 respectively

At the moment when the 1st cyclist

he goes the distance

half a circle more

The speed of one is 21 km/h greater than the speed of the second - this means that the speed in pursuit is 21 km/h.

Let's find out how long it takes for him to eliminate the difference of 7 km (this is exactly the distance between them initially - half a circle from 14 km of the entire route).

7:21 = 1/3 (h)

It remains to convert 1/3 hour into minutes - that’s 20 minutes.

You need to understand that in these 20 minutes the motorcyclist will not travel 7 km (!), but maybe more than a circle.

one circle more.

3. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 14 km. How many minutes will it take for motorcyclists to meet each other for the first time if the speed of one

one of them is 21 km/h more than the other?

7 km less (half a circle)

15 km less (1 lap)

t(x+21)

2 blue

2 green

x we get in hours.

The speed of one is 21 km/h greater than the speed of the second - this means that the speed in pursuit is 21 km/h.

Let's find out how long it takes for him to eliminate the difference of 7 km (this is exactly the distance between them initially - half a circle from 14 km of the entire route).

7:21 = 1/3 (h)

It remains to convert 1/3 hour into minutes - that’s 20 minutes.

You need to understand that in these 20 minutes the motorcyclist will not travel 7 km (!), but maybe more than a circle.

How many laps did you drive?

every motorcyclist

it doesn't matter to us. It is important that blue traveled half a circle more to the meeting point, i.e. at 7 km.

one circle more.

Let the full circle be 1 part.

4. Ski competitions take place on a circular track. The first skier completes one lap for 2 minutes faster than second and an hour later he is ahead of the second by exactly one lap. How many minutes does it take the second skier to complete one lap?

This condition will help you enter x...

First, let's express the speed of each skier. Let the first skier complete a circle in x minutes. The second one is 2 minutes longer, i.e. x+2.

parts/min

Part

1 skier

2 skier

lap/min

1 lap more

1 skier

2 skier

– = 1

80 km/h, and 40 minutes after the start he was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

14 km more (1 lap)

1 yellow

2 blue

2 green

To find the speed of the second car, divide the distance it has traveled 50 km by a time of 40 minutes (hours).

one circle more.

5. From one point on a circular track, the length of which is 14 km, two cars started simultaneously in the same direction. The speed of the first car is 80 km/h, and 40 minutes after the start he was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

14 km more (1 lap)

1 yellow

2 blue

2 green

1) 80 *(2/3)= 160/3=53(1/3) (km) the first car drove in 40 minutes. This is 1 lap more than the distance covered by the second car, i.e. at 14 km.

2) 53(1/3) – 14 = 39(1/3) (km) traveled by the second car in 40 minutes.

To find the speed of the second car, divide the distance it has traveled 50 km by a time of 40 minutes (hours).

3) 39(1/3) : (2/3) = 59 (km/h)

Answer: The speed of the second car is 59 km/h.

It was possible to first find the speed to catch up: 80 – x

Then the equation will look like this:

one circle more.

You can press the button several times. How many laps did each car drive for us?

doesn't matter. It is important that the yellow car drove 1 lap more, i.e. at 14 km.

6. A cyclist left point A of the circular route, and 30 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time.

Find the speed of the motorcyclist

if the length of the route is 30 km.

Give your answer in km/h.

1 meeting. The cyclist was 40 minutes (2/3 hours) before the first meeting, the motorcyclist was 10 minutes (1/6 hours). And during this time they traveled the same distance.

1 motorcycle.

2 bicycles

1 equation:

one circle more.

Give your answer in km/h.

2nd meeting. A cyclist and a motorcyclist were on their way

until the 2nd meeting 30 minutes (1/2 hour).

And during this time the motorcyclist traveled 1 lap more.

30 km more (1 lap)

1 motorcycle.

You can write the equation in another way.

2 bicycles

2 equation:

The required value is x

Show (2)

7. The clock with hands shows 8 hours 00 minutes. In how many minutes will the minute hand line up with the hour hand for the fourth time?

a circle more

lap/h

circle

a circle more

minute

hourly

1x – =

Answer: 240 min

Examination

The first time the minute hand needs

walk more laps to catch up with the minute hand.

The 2nd time – 1 more lap.

The 3rd time – 1 more lap.

The 4th time – 1 more lap.

a circle more

The minute hand catches up with the hour hand once every hour. The last, fourth time will catch up at 12:00, i.e. in 4 hours, or 240 minutes.

Show (4)

Another way is in the comments.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

The motorcyclist's path and the cyclist's path

are equal, the cyclist rode 40 minutes,

The motorcyclist drove 10 minutes.

Caught up in 10 minutes

In 30 minutes

Since the motorcyclist caught up with the cyclist after 10 minutes, their distances are equal.

x km/h – bicycle speed, y km/h – motor speed.

The length of the route is 30 km, because the motorcyclist caught up with the cyclist for the second time, then they covered S km in 30 minutes, then the motorcyclist’s distance in 0.5 hours is (S+30), and the cyclist’s is S km.

This means the motorcyclist’s path is 30+10=40 km.

v(mot)= 40:0.5=80 km/h

Answer: 80 km/h

Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 14 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 21 km/h greater than the speed of the other?

One of them drove half a circle

more, that is, 7 km more.

How many minutes later will they

Matching for the first time?

One of them drove half a circle more, that is

Consider the movement of two points along a circle of length s in one direction while simultaneously starting at speeds v 1 andv 2 (v 1 >v 2) and answer the question: after what time will the first point be ahead of the second by exactly one circle? Assuming that the second point is at rest and the first is approaching it with speed v 1 –v2., we find that the condition of the problem will be fulfilled when the first point is equal to the second for the first time. In this case, the first point will travel a distance equal to length one circle, and the required formula is no different from the formula obtained for the task of chasing after movement:

So, if two points simultaneously begin to move around a circle in one direction with speeds v 1 and v 2, respectively (v 1 > v 2, respectively), then the first point approaches the second with speed v 1 —v 2 and at the moment when the first point catches up with the second for the first time, it covers a distance of one circle more.

Problem 3.

From one point on a circular track, the length of which is 14 km, two cars started simultaneously in the same direction. The speed of the first car is 80 km/h, and 40 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h. Let the speed of the second car be x km/h. Since 40 minutes is 2/3 of an hour and this is the time during which the first car will be ahead of the second by one lap, we will draw up the equation according to the conditions of the problem

where 160 - 2x = 42, i.e. x = 59.

Answer. 59 km/h

Training tasks

T3.1. From one point on a circular track, the length of which is 15 km, two cars started simultaneously in the same direction. The speed of the first car is 60 km/h, the speed of the second is 80 km/h. How many minutes will pass from the start before the first car is exactly 1 lap ahead of the second?

T3.2. From one point on a circular track, the length of which is 10 km, two cars started simultaneously in the same direction. The speed of the first car is 90 km/h, and 40 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

T3.3. Two motorcycles start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 20 km. How many minutes will it take for the motorcycles to meet each other for the first time if the speed of one of them is 12 km/h greater than the speed of the other?

T3.4. The clock with hands shows 9 hours 00 minutes. In how many minutes will the minute hand line up with the hour hand for the third time?

T3.5. Ski competitions take place on a circular track. The first skier completes one lap 2 minutes faster than the second and an hour later is exactly one lap ahead of the second. How many minutes does it take the second skier to complete one lap?

T3.6. Two bodies move in a circle in one direction. The first one completes the circle 3 minutes faster than the second one and catches up with the second one every hour and a half. How many minutes does it take the first body to complete one circle?

T3.7. Two points rotate uniformly in a circle. The first makes a revolution 5 seconds faster than the second and makes 2 more revolutions per minute than the second. How many revolutions per minute does the second point make?

T3.8. From point A of the circular track they simultaneously begin uniform motion two bodies in opposite directions. At the moment of their meeting, the first body travels 100 meters more than the second and returns to point A 9 minutes after the meeting. Find the length of the path in meters if the second body returns to point A 16 minutes after the meeting.

More than 80,000 real problems of the Unified State Exam 2019

You are not logged in to the system "". This does not interfere with viewing and solving tasks Open Bank of Unified State Examination Problems in Mathematics, but to participate in the user competition to solve these tasks.

Search result for Unified State Exam assignments in mathematics for the query:
« A bicycle left point A of the circular track» — 251 tasks found

Task B14 ()

(views: 605 , answers: 13 )

Task B14 ()

(views: 624 , answers: 11 )

The correct answer has not yet been determined

Task B14 ()

(views: 691 , answers: 11 )

Answer: 60

Task B14 ()

(views: 612 , answers: 11 )

The correct answer has not yet been determined

Task B14 ()

(views: 608 , answers: 9 )

The correct answer has not yet been determined

Task B14 ()

(views: 618 , answers: 9 )

The correct answer has not yet been determined

Task B14 ()

(views: 610 , answers: 9 )

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 26 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 39 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 622 , answers: 9 )

The correct answer has not yet been determined

Task B14 (

1. Two cars left point A to point B at the same time. The first one drove at a constant speed all the way. The second car traveled the first half of the journey at a speed lower than the speed of the first by 15 km/h, and the second half of the journey at a speed of 90 km/h, as a result of which it arrived at point B at the same time as the first car. Find the speed of the first car if it is known to be greater than 54 km/h. Give your answer in km/h.

2. A train, moving uniformly at a speed of 60 km/h, passes a forest belt, the length of which is 400 meters, in 1 minute. Find the length of the train in meters.

3. The distance between cities A and B is 435 km. The first car drove from city A to city B at a speed of 60 km/h, and an hour after that the second car drove towards it at a speed of 65 km/h. At what distance from city A will the cars meet? Give your answer in kilometers.

4. A freight train and a passenger train travel along two parallel railway tracks in the same direction at speeds of 40 km/h and 100 km/h, respectively. The length of a freight train is 750 m. Find the length of a passenger train if the time it takes to pass the freight train is 1 minute.

5. A train, moving uniformly at a speed of 63 km/h, passes a pedestrian walking in the same direction parallel to the tracks at a speed of 3 km/h in 57 seconds. Find the length of the train in meters.

6. Solving motion problems.

7. The road between points A and B consists of ascent and descent, and its length is 8 km. The pedestrian walked from A to B in 2 hours 45 minutes. The time it took to descend was 1 hour and 15 minutes. At what speed did the pedestrian walk downhill if his speed on the uphill is 2 km/h less than the speed on the downhill? Express your answer in km/h.

8. The car traveled from the city to the village in 3 hours. If he increased his speed by 25 km/h, he would spend 1 hour less on this journey. How many kilometers is the distance from the city to the village?

http://youtu.be/x64JkS0XcrU

9. Ski competitions take place on a circular track. The first skier completes one lap 2 minutes faster than the second and an hour later is exactly one lap ahead of the second. How many minutes does it take the second skier to complete one lap?

10. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 6 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 18 km/h greater than the speed of the other?

Movement problems from Anna Denisova. Website http://easy-physics.ru/

11. Video lecture. 11 movement problems.

1. A cyclist travels 500 m less every minute than a motorcyclist, so he spends 2 hours more on a journey of 120 km. Find the speeds of the cyclist and motorcyclist.

2. A motorcyclist stopped to refuel for 12 minutes. After that, increasing the speed by 15 km/h, he caught up Lost time at a distance of 60 km. How fast was he moving after stopping?

3. Two motorcyclists set off simultaneously towards each other from points A and B, the distance between which is 600 km. While the first one covers 250 km, the second one manages to cover 200 km. Find the speed of motorcyclists if the first one arrives in B three hours earlier than the second one in A.

4. The plane was flying at a speed of 220 km/h. When he had 385 km less to fly than he had already covered, the plane increased its speed to 330 km/h. The average speed of the aircraft along the entire route turned out to be 250 km/h. How far did the plane fly before its speed increased?

5. By railway the distance from A to B is 88 km, by water it increases to 108 km. The train from A leaves 1 hour later than the ship and arrives at B 15 minutes earlier. Find the average speed of the train, if it is known that it is 40 km/h greater than the average speed of the ship.

6. Two cyclists left two places 270 km apart and are traveling towards each other. The second travels 1.5 km less per hour than the first, and meets him after as many hours as the first travels in kilometers per hour. Determine the speed of each cyclist.

7. Two trains depart from points A and B towards each other. If the train from A leaves two hours earlier than the train from B, then they will meet halfway. If they leave at the same time, then after two hours the distance between them will be 0.25 of the distance between points A and B. How many hours does each train take to complete the entire journey?

8. The train passed a person standing motionless on the platform in 6 s, and passed a platform 150 m long in 15 s. Find the speed of the train and its length.

9. A train 1 km long passed the pole in 1 minute, and through the tunnel (from the entrance of the locomotive to the exit of the last car) at the same speed in 3 minutes. What is the length of the tunnel (in km)?

10. Freight and fast trains departed simultaneously from stations A and B, the distance between which is 75 km, and met half an hour later. The freight train arrived at B 25 minutes later than the fast train at A. What is the speed of each train?

11. Piers A and B are located on a river whose current speed in this section is 4 km/h. The boat goes from A to B and back without stopping average speed 6 km/h. Find the boat's own speed.

12. Video lecture. 8 problems for moving in a circle

12. Two points move uniformly and in the same direction along a circle 60 m long. One of them makes a full revolution 5 seconds faster than the other. In this case, the points coincide every time after 1 minute. Find the speeds of the points.

13. How much time passes between two consecutive coincidences of the hour and minute hands on a watch dial?

14. Two runners start from one point on the stadium ring track, and the third - from a diametrically opposite point at the same time as them in the same direction. After running three laps, the third runner caught up with the second. Two and a half minutes later, the first runner caught up with the third. How many laps per minute does the second runner run if the first one overtakes him once every 6 minutes?

15. Three racers start simultaneously from one point on a track shaped like a circle and ride in the same direction at constant speeds. The first rider overtook the second for the first time, making his fifth lap, at a point diametrically opposite to the start, and half an hour after that he overtook the third rider for the second time, not counting the start. The second rider caught up with the third for the first time three hours after the start. How many laps per hour does the first driver make if the second driver completes the lap in at least 20 minutes?

16. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 14 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 21 km/h greater than the speed of the other?

17. A cyclist left point A of the circular route, and 30 minutes later a motorcyclist followed him. In 10 minutes. after leaving, he caught up with the cyclist for the first time, and 30 minutes later he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

18. A clock with hands shows 3 o’clock exactly. In how many minutes will the minute hand line up with the hour hand for the ninth time?

18.1 Two riders race. They will have to drive 60 laps along a 3 km long ring track. Both riders started at the same time, and the first one reached the finish line 10 minutes earlier than the second one. What was the average speed of the second driver, if it is known that the first driver overtook the second driver for the first time in 15 minutes?

13. Video lecture. 6 problems for moving on water.

19. Cities A and B are located on the banks of a river, with city B downstream. At 9 o'clock in the morning a raft leaves from city A to city B. At the same moment, a boat departs from B to A and meets the raft 5 hours later. Having reached city A, the boat turns back and sails to B at the same time as the raft. Will the boat and raft have time to arrive in city B by nine o'clock in the evening of the same day?

20. A motor boat left from point A to point B against the flow of the river. On the way, the engine broke down, and while it took 20 minutes to repair it, the boat was carried down the river. Determine how much later the boat arrived at point B, if the journey from A to B usually takes one and a half times longer than from B to A?

21. Cities A and B are located on the banks of a river, with city A downstream. From these cities two boats leave at the same time towards each other and meet in the middle between the cities. After the meeting, the boats continue their journey, and, having reached cities A and B, respectively, turn around and meet again at a distance of 20 km from the place of the first meeting. If the boats initially swam against the current, then the boat that left A would catch up with the boat that left B, 150 km from B. Find the distance between the cities.

22. Two steamships, the speed of which is the same in still water, depart from two piers: the first from A downstream, the second from B upstream. Each ship stays at its destination for 45 minutes and returns. If the steamships depart simultaneously from their starting points, then they meet at point K, which is twice closer to A than to B. If the first steamship departs from A 1 hour later than the second one departs from B, then on the way back the steamships meet 20 km from A. If the first steamboat leaves from A 30 minutes earlier than the second from B, then on the way back they meet 5 km above K. Find the speed of the river and the time it takes the second steamboat to reach from A to TO.

23. A raft set off from point A to point B, located downstream of the river. At the same time, a boat came out to meet him from point B. Having met the raft, the boat immediately turned and sailed back. How far from A to B will the raft travel by the time the boat returns to point B, if the speed of the boat in still water is four times the speed of the current?

24. Piers A and B are located on a river whose current speed in this section is 4 km/h. A boat travels from A to B and back at an average speed of 6 km/h. Find the boat's own speed.

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