Problem is from Classical Mechanics:
I am a beginner in Physics trying to understand the solution to the given below problem.
Problem Statement: 3 particles are placed at the vertices of an equilateral triangle ABC, the length of each side of the triangle is s, and the particles are moving towards each other at a constant velocity v. At every movement the particle is moving toward the particle which is right to it (in counter-clockwise direction) i.e. A always has its velocity along AB, B along BC and C along CA. How long does it take for particles to meet at centroid c.
Below are the illustration of the trajectories of the particles, when approaching each other:
I know the answer by looking at how the other people solved the problem, but I am quite unable to understand the answer which are given in the following links:
- Why do three particles placed at the vertices of an equilateral triangle, moving along the sides, meet at the centroid?
- When do 3 particles on the vertices of an Equilateral triangle meet?
So, after solving I am more interested in generalizing the scenario from triangle to any n-sided polygon? Like how can we approach to solve a problem if I am asked the same scenario but instead of 3 particles, there will be 4 particles placed at the corners of the square or what if it is a n-sided polygon with n particles placed on the n corners, would the answer dependent on the geometrical construction or will remain the same?