I also cross-posted this on another website ("http://www.dance.net/topic/5577521/1/Homework-Help/Physics-dilemma-Elastic-Collisions.html" [Broken]), so I'll just copy & paste. I got three completely different answers while using equally legitimate formulas (formulae)? This is on elastic collisions. Here's the original problem. It is a purely elastic collision, so there's no energy lost to heat or any of that... A 7 kg bowling ball traveling at an unknown speed knocks over a 2 kg bowling pin at rest. After the collision, the bowling ball is traveling at 1.8 m/s, while the bowling pin flies off at 3.0 m/s. I used the conservation of momentum equation: m1v1 + m2v2 = m1v1' + m2v2', and found v1 (the desired) to be 2.66 m/s, which is the correct answer. But... I also tried the conservation of kinetic energy equation: (1/2)(m1v1^2) + (1/2)(m2v2^2) = (1/2)(m1v1'^2) + (1/2)(m2v2'^2), and found v1 to be 2.4 m/s I tried the equation derived from both the conservation of momentum and the conservation of kinetic energy: v1 + v1' = v2 + v2' (Do I have to show how I derived it? It's in both my physics book from Giancoli and Barron's review book for AP Physics B) and found v1 to be 1.2 m/s. I don't think it's a directional problem, since the direction of motion is the same for both. My AP Physics teacher thinks she needs to "mull" over the question a bit. My mom thinks there has to be some limitation on the versatility of the v1 + v1' = v2 + v2' equation...Well, I just can't seem to give a reasonable explanation for getting three different answers out of perfectly legitimate equations. Help, anyone? ~H.