determine the center of mass for three particles(1.5, 2.5, 3.5) forming a equilateral triangle one side lenght of 135cm.

To determine the center of mass for three particles forming an equilateral triangle, we need to find the coordinates of the center of the triangle and calculate the average of the coordinates of the three particles.

Step 1: Find the coordinates of the center of the triangle:
Since the triangle is equilateral, we can assume one of the particles as the origin (0, 0).
Let's assume the particle at coordinates (0, 0) as particle A.
Given that the side length of the equilateral triangle is 135 cm, the distance from particle A to any of the other two particles is 135 cm.

Using trigonometry, we can calculate the coordinates of the other two particles based on the distance and angles.

The angle at particle A (0, 0) is 120 degrees (360 degrees / 3 particles).
To find the coordinates of particle B:
- The x-coordinate of particle B will be 135 * cos(120°)
- The y-coordinate of particle B will be 135 * sin(120°)

To find the coordinates of particle C:
- The x-coordinate of particle C will be 135 * cos(240°)
- The y-coordinate of particle C will be 135 * sin(240°)

Step 2: Calculate the center of mass:
To calculate the center of mass, we need to find the average of the x-coordinates and the average of the y-coordinates of the three particles.

Let's assume the three particles have coordinates:
A (0, 0)
B (x1, y1)
C (x2, y2)

The x-coordinate of the center of mass (CMx) will be (0 + x1 + x2) / 3
The y-coordinate of the center of mass (CMy) will be (0 + y1 + y2) / 3

By substituting the coordinates of particles B and C, we can calculate the coordinates of the center of mass.