BRAINCAKEResolving Momentum in Collisions
Most two-dimensional collision problems are solved by resolving every momentum into two perpendicular components and applying conservation of momentum to each direction separately.
Method:
1. Choose axes, usually with x along the initial direction of motion.
2. Resolve each momentum into components: px = p cosθ and py = p sinθ, giving each a sign (+ or –).
3. Write two equations: total px before = total px after, and total py before = total py after.
4. Solve for the unknown components, then combine them using Pythagoras (magnitude) and tan (direction).
If an object moving along x hits a stationary object, the total y-momentum before is zero. So after the collision the y-components must add up to zero: the two objects move off on opposite sides of the original line.
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