A cart with a mass of 340 g moving on a frictionless linear air track at an initial speed of 1.2 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the rst cart continues in the same direction at 0.66 m/s. (a) What is the mass of the second cart? (b) What is its speed after the collision? I have two equations: Conservation of Momentum and Conservation of KE (since this is elastic). m1vi = m1v1 + m2v2 .5m1vi2 = .5m1v12 + .5m2v22 I've solved for v2 using the equation for Conservation of Momentum, and plugged that into the equation for Conservation of KE and my answer is wrong (used up about a page of algebra, please don't expect me to type it out all on here). The correct answer can be found using the method in the PDF below. http://www.physics.ucc.ie/py1052_ps6.pdf (problem 8) My issue is that they solve for v1f (or as I called it in the equations above, v1) and yet v2f (or v2) is nowhere to be found on the side opposite of their v1f. I don't see how their algebra makes any sense. All I want is someone to explain this to me as this is supposed to be a straightforward question.