Question

suppose that v1x and v2x have equal magnitudes. also, v1→ is directed to the right and v2→ is directed to the left. the velocity of the center of mass is then:

Answer 1

The x-component of the centre of mass velocity would be zero because the contributions to momentum along the x-axis from two equal and opposite velocities cancel each other out.

Step-by-step explanation:

When calculating the velocity of the centre of mass (vCM), we rely on the concept of conservation of momentum and the knowledge that velocity is a vector quantity with both magnitude and direction. If two particles have equal masses and their velocities along the x-axis (v1x and v2x) have equal magnitudes but opposite directions (right for v1→ and left for v2→), their contributions to the total momentum along the x-axis cancel each other out. Therefore, the x-component of the centre of mass velocity would be zero since v1x + (-v2x) = 0. It's important to note that if no external forces are acting on the system along the x-axis, the centre of mass of a system continues to move at constant velocity.