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

1. Since the two cars are moving head-on so here we can say the zero momentum of the reference will the the reference of centre of mass of the car

so here speed of centre of mass will be

V = (m1v1+ m2v2) / (m1+ m2)

here m1 = m2 = m

v1 = v and v2 = -v

V = [mv + (-mv)] / (m+m) = 0

here the speed of that reference frame will be zero

ii) Now if both the cars is moving in same direction then reference of centre of mass of the car

we can use the same formula

V = (m1v1+ m2v2) / (m1+ m2)

here m1 = m2 = m

v1 = v and v2 = v

V = mv + mv / (m+m) = v/2

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