Relative velocity and closing speed

In Physics simulations or game engines it’s sometimes useful to determine the speed with which two objects are approaching each other. This post will discuss the concept of closing speed, which is the normal component of the relative velocity of two objects. Relative velocity and its components Suppose we have objects A and B [1] with velocity vectors \vec{V_A} and \vec{V_B}. The relative velocity of B w.r.t. A is: \[\vec{V}_{B|A}=\vec{V}_B-\vec{V}_A\] Put differently, it’s the velocity of B in…