Final answer:
The x-component of the center of mass velocity for equal mass particles moving along the x-axis is the average of the x-components of their individual velocities. Given that one particle's velocity component is V1x and the other's is V2x, the center of mass velocity is calculated by (V₁x + V₂x) / 2.
Step-by-step explanation:
To determine the x-component of the center of mass velocity (vcm)x, we need to consider the velocities of individual masses and their respective contributions. In the situation where two blocks, or particles, move along the x-axis, the (vcm)x can be found by taking the average of the x-components of their velocities if the masses are equal. This assumption is made clear in some of the information provided: 'Since both cars have equal mass...'
Furthermore, the x-components of the velocities have the form v cos(θ), and when a particle moves directly along the x-axis, this becomes simply V1x = V1 because the cosine of 0 degrees is 1. To find the x-component of the center of mass velocity, we simply use the following formula, given that the masses are equal:
(vcm)x = (V₁x + V₂x) / 2
For example, if one block is moving at V₁ = 40 m/s, and the other is at rest (V₂x = 0 m/s), the vcm)x would be (40 + 0) / 2 = 20 m/s. This is an application of conservation of momentum in the context of center of mass calculations.