Question: Consider a circular field with radius 1 kilometer. Inside the field, there are two goats, Goat A and Goat B, initially positioned at two different points on the circumference of the field. The goats start moving simultaneously along the circumference of the field at a constant speed of 100 meters per minute in the clockwise direction. Goat A moves at a constant angular speed of 1 radian per minute, while Goat B moves at a constant angular speed of 2 radians per minute.

Now, let's define the following scenario: Goat B wants to catch up with Goat A and be at the same point on the circumference of the field at the same time. However, as soon as Goat B reaches the point where Goat A is located, Goat A senses it and instantly changes its direction, moving in the opposite (counterclockwise) direction at the same constant speed and angular speed as before.

Given this scenario, answer the following questions:

How long does it take for Goat B to catch up with Goat A for the first time? Provide your answer in minutes and seconds.

After Goat B catches up with Goat A, how many times will the goats meet or cross each other before they both complete exactly one full revolution around the field?

How far will each goat have traveled (in meters) from the starting point when they meet for the second time?

Suppose the radius of the circular field is doubled to 2 kilometers, but the speeds and angular speeds of the goats remain the same. Will the answers to the previous questions change? Explain your reasoning.

Note: You may assume that the goats can instantly change their direction without any delay or loss of speed.

Please note that although the problem statement is long, the actual question is composed of the four sub-questions listed above.

Please note : No use Chatgpt ( getting wrong answer i need correct answer otherwase i will dislike )!!