Interesting problems

Find this critical angular velocity.

Problem 2.

Fox (missile) observes rabbit (plane) moving with speed v on the distance L and start to move directly on the target with the speed V.

Find the time when the fox catches the rabbit.

Problem 3.

Beetle creeps on rubber. When the beetle has creeped the distance l

the rubber are lengthening by the distance L (NB: beetle sit on the rubber).

The beetle has creeped the distance l again,

and the rubber are lengthening by the distance L again.

Does the beetle reach the end of the rubber? (l << L)

If yes, how many steps N has to be done before the beetle reachs the end of the rubber?

Problem 4.

Similar problem, but beetle creeps on rubber with speed v, and rubber elongated with speed V.

Does the beetle reach the end of the rubber? If yes, how long beetle need to reach the end of the rubber?

Problem 5.

1. There are 5 houses with different colors.

2. Each house has a resident with a different nationality.

3. Each person has one favorite drink, one type of cigarette, and one type of animal, different from the others.

You should also know that:

1. The English man lives in the crimson house.

2. The Swedish man has a dog.

3. The Dutch man drinks tea.

4. The green house is located on the left side near the white house.

5. The person living in the green house drinks tea.

6. The person smoking «Pall Mall» has a bird.

7. The person living in the central house drinks milk.

8. The person from yellow house smokes «Dunhill».

9. The Norwegian lives in the 1-st house.

10. The person smoking «Marlboro» lives near the person that has a cat.

11. The person that has a horse lives near the person that smokes «Dunhill».

12. The person smoking «Winfield» drinks beer.

13. The Norwegian lives near the blue house.

14. The German smokes «Rothmans».

15. The person who smokes «Marlboro» lives near the person that drinks water.

Which person has a fish?

Problem 6.

Two friends, John and Smith, do not meet each other a long time and they decide to go and have lunch together after work.

While having lunch John asks Smith about his life.

- I have married and I have 3 sons.

- How old are your sons?

- Sum of their ages is today's date.

- OK. What else?

- If you multiply their ages, the number is equal to my age.

- I still need more clue.

- My middle son like to dance.

- Now I got it.

How old are Smith's sons?

Problem 7.

Four towns located in the vertex of square with side a. They should be connected with minimal length road.

How the road should pass and what is the length of the road?

Problem 8.

In the figure shown below, the centers of the circles C₀(R), C₁ (R₁), and C₂ (R₂) are co-linear, A and B are the points of intersection of C₁ and C₂, and C is a point of intersection of C₀ and the extension of AB.

Find the radii of two small circles shown (r₁, r₂), tangent to C₀, C₁ and BC, and to C₀, C₂ and BC, respectively.

You can check your answer in answers.

If you are interested in details of the solution contact me.

To be continued.