Question

six particles situated at the corners of a regular hexagon of side a move at a constant speed v each particle maintain a direction towards the particle at the next corner. the time taken by the particles to meet each other is

Answer 1

2 answers · Physics

Best Answer
A regular hexagon is composed of 6 equilateral triangles. One side of each triangle forms a chord of the circumscribed circle, while the other two sides are radii of the circle. Each chord therefore intersects the circle at a 30° angle.

The radial component of the speed is given by the sine of the angle times the speed. The sine of 30° is 0.5, so the radial speed is v/2.

The time for the particles to meet is thus 2r/v.


Answers
a hexagon of side A is made up of an adjacent group of 6 equilateral triangles of side A

assume particles numbered from 1 to 6
at (A,0), (0.5A,0.866A), (-0.5A,0.866A), (-A,0), (-0.5A,-0.866A), (0.5A,-0.866A)

particle 1 initially moves at V<60 toward particle 2
particle 2 initially moves at V<180 towards particle 3
The motion of particle 2 can be broken into components parallel to and normal to particle 1
the normal component = V sin(30) = 0.5V

This will cause the hexagon to rotate and shrink as each particle spirals to the center .
but I can't think of the next equation