## more math (coalesce notes)October 24

m1v1 + m2v2 = m1v1f + m2v2f

m1v1f = m1v1 + m2v2 - m2v2f

m1v1f = m1v1 + m2(v2 - v2f) * v1f = (m1v1 + m2(v2 - v2f)) / m1 Then solve for v2f in the other equation & substitute? where exactly does the cosθ come from? I'd have to figure that out, anyways, and I'm not 100% sure how. (Hell, I don't have a clue.) m1v12 + m2v22 / 2 = ... wait ... why the x/2? Both sides of the equation are divided by 2. Couldn't I just get rid of it? The answer to that, of course, is yes. but basically I'm solving for 4 unknowns. 2 vectors = 2 sets of 2 values each. Either force + angle or dx + dy. And I can convert between those. m1v12 + m2v22 / 2 = m1v1f2 / 2 + m2v2f2 m1(v12 - v1f2) = m2(v22 - v2f2) m1(v12 - v1f2) / m2 = v22 - v2f2 v2f2 = v22 - m1(v12 - v1f2) / m2

So I should treat all collisions (that don't destroy both objects) as collisions between spherical objects, at least as far as determining the post-collision movement vectors. Then I need to determine the line connecting their centers, and calculate the objects' movement vectors (x,y components) relative to that line. The y component will remain unchanged. [some notes pertaining to a graph that won't make sense w/o the image] v1f =

• v1 + m2(v2 - (v22 - m1(v12 - v1f2) / m2))) / m1 [sic]
• v1 + m2(v2 - (v22 - (m1v12 - m1v1f2) / m2)) / m1
• v1 + m2v2 - m2(v22 - (m1v12 - m1v1f2) / m2) / m1
• v1 + m2v2 - (m2v22 + m1v12 - m1v1f2) / m1
• v1 + m2v2 - m2v22 / m1 + v12 - v1f2
• v1f + v1f2 = v1 + m2v2 - m2v22 / m1 + v12
• [this next equation looks wrong]

this doesn't help me! a2 + b2 = c2 ? (Do I know either a or b? I don't think I do.) This can't be that hard. Hell, if it helps I can even tweak the equation so one body is at "rest". I need a good geometry / physics book. But I can't. I'm already behind on my bills. There's the internet, granted, but that's not the same. [many more trig. notes that would be useless w/o the diagrams accompanying]