Question

Six particles situated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.

Answer 1

The particles meet at the centroid O of the triangle. At any instant the particles will form an equilateral ΔABC with the same centroid. Consider the motion of particle A. At any instant its velocity makes angle 30°. This component is the rate of decrease of the distance AO.