### Chapter 13, “Momentum and Collisions”

#### Axis-Aligned Vector Reflection

If the stationary boundary is vertical, v_{f} = [–v_{ix}
v_{iy}] and if the stationary boundary is horizontal, v_{f} = [v_{ix} –v_{iy}] for incoming velocity v_{i} = [v_{ix}
v_{iy}].

#### Non-Axis-Aligned Vector Reflection

v_{f} = 2 * P + v_{i}

where v_{i} = the incoming velocity and P = the projection of –v_{i} onto the normal of the boundary line.

#### Momentum

p = mv

where m = mass and v = velocity.

#### Impulse

Impulse = Ft

where F = net force and t = a very small amount of time.

#### Impulse-Momentum Theorem

Impulse = Ft = (Δp)

where F = net force, t = a very small amount of time, and p = momentum.

#### Conservation of Momentum Theorem

m_{1}v_{1i} + m_{2}v_{2i} = m_{1}v_{1f} + m_{2}v_{2f}

where the 1 subscript represents object 1 and the 2 subscript represents ...