Most Collisions Are Secretly in One Dimension

• When two objects collide there is typically a single point on a surface which intersects another surface; this results in a single ray which is the axis of collision.
• Most collisions happen exclusively on this axis, and so, happen in "one dimension."

Conservation of momentum: m1v1 + m2v2 = m1u1 + m2u2

Conservation of energy: m1 v2^2 + m2 v2^2 = m1 u1^2 + m2 u2 ^2

Typically mass of an object and velocity of the object apportions how much of the energy ends up on what object is in the collision.

Some energy is lost from the collision and becomes some other carrier (sound, infrared, etc) or becomes angular momentum.

Complex collisions are typically smaller objects having their own one on one collisions which then probablistically happen on a single dimension.