Two identical cars approach each other head-on while traveling at the same speed

Question

Two identical cars approach each other head-on while traveling at the same speedv.

Part A

What does an observer in the Earth reference frame measure for the speed of the zero-momentum reference frame of this two-car system?

Express your answer in terms of v.

vzeroframe =

Part B

Suppose the same cars are traveling in the same direction at the same speed v. Now what does an observer in the Earth reference frame measure for the speed of the zero-momentum reference frame?

Express your answer in terms of v.

vzeroframe =

Explanation / Answer

In all zero momwntum reference frames, the center of mass is at rest

in case when two identical cars approaching each other with same speed, then their center of mass will remain unchanged because of the symmetry, so

since the center of mass is alreadt at rest so velocity of the zero momentum reference frame will also be 0

vzeroframe = 0 m/s

in second case when both the cars are moving in same direction with same speed, thenthe center of mass will also be movinf with the same speed v

in order to mke center of mass at rest with respect to zero momentum reference frame, it also must have same velocity v, so,

vzeroframe = v m/s

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