# Elastic collision: Help solving for unknowns

Is it possible to solve for an elastic collision when vb and v'a are the two unknowns? I have been trying for a few hours to solve for either unknown using the conservation of momentum and the conservation of total kinetic energy equations but have come up with nothing. Can anyone help?

mava +mbvb = mav'a + mbv'b

1/2mav2a +1/2mbv2b = 1/2mav'2a + 1/2mbv'2b

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Hmmm. That equation there is not solvable unless you have another equation you can eliminate one of the unknown variables with.

Look carefully at the question and see if there any other information you can glean from it. For example, is it implied that one of the velocities is zero at any time? It might also help to write out the problem in full so someone can have a crack at it.

Nothing is implied about the second ball being at rest on collision. The problem states that two balls have a head on elastic collision. Ball (a) has a mass of 0.02kg and is moving at 3.0 m/s in the +x. Ball (b) has a mass of 0.035kg and a final velocity of 1.5m/s in the +x. I'm trying to find the initial velocity of ball (b) and the final velocity of (a). I have spent hours trying to come up with an equation through substitution that will get me either of the two unknowns but have not been able to figure anything out.

Anyone have any ideas? I have asked multiple friend for help and nobody seems to know how to work this problem. This assignment is due tomorrow.

Thank you in advance for any help