# Velocity and frame of reference question

Hey I am just lookin for some guidance here of what equations to use for this problem. My teacher gave us likea hint, but the hints are from the book used in the previous course and since i am a transfer stuident, i do not have this book. Anyway the question goes as followed....

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

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By definition elastic collision implies that kinetic energy is conserved. Hence I couldn't understand the meaning in the question C and F. Can anyone explain? Is the need to verify the formula of finding final velocities after elastic collision.

vaishakh said:
By definition elastic collision implies that kinetic energy is conserved. Hence I couldn't understand the meaning in the question C and F. Can anyone explain? Is the need to verify the formula of finding final velocities after elastic collision.
I think the question is hinting in that Energy conservation applies no matter what frame of reference you use. So its asking you to prove it.

Sam

I think you know what is elastic collision. You can write two equations for elastic collisions.
M1u1 + m2u2 = m2v2 +m1v1 – momentum conservation
M1u1^2 + m2u2^2 = m1v1^2 + m2v2^2 – energy conservation
Try to solve these simultaneous equations and get v1 and v2 with respect to m1, m2, u1 and u2.