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You are driving a bumper car (total mass = 155 kg) at +12.0 m/s in the positive x-direction (in the reference frame of the Earth), toward your friend (in his bumper car, total mass 125 kg) who is driving in the same direction at +6.00 m/s (in the reference frame of the Earth). You collide elastically.

To get you started, in your reference frame (a reference frame in which you are at rest with v = 0), the initial velocity of your friend (before the collision) is -6.00 m/s; you see your friend coming toward you (negative x-direction) at 6.00 m/s.

A) In your friend's reference frame (a reference frame in which your friend is at rest), what is your initial velocity (before the collision)?

B) Analyze the collision in your (initial) reference frame (moving at +12.0 m/s in the x-direction with respect to the reference frame of the Earth). What are the final velocities (after the collision) of you and your friend in this reference frame? You can use eqns. 9.22 and 9.23 in the text for this.

C) Show that the total kinetic energy of you and your friend was conserved in this reference frame, i.e. that equation 9.16 in the text is true.

D) Show that the total linear momentum of you and your friend was conserved in this reference frame, i.e. that equation 9.15 in the text is true.

E) In the reference frame of the Earth, what are the final velocities (after the collision) of you and your friend? You may simply transform the velocities you calculated in (B) back to the Earth's reference frame.

F) Show that the total kinetic energy of you and your friend was conserved in the Earth's reference frame.

G) Show that the total linear momentum of you and your friend was conserved in the Earth's reference frame.

I am just lookin for some guidance of which equations i need to be lookin at for parts B, C, F, and G. Thanks