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 and . The relative velocity of B w.r.t. A is: Put differently, it’s the velocity of B in A’s frame of reference. This relative velocity is a vector, and we can split it into orthogonal components. Obviously, the nature of such a split depends on the basis we want to use. We could look at the vector’s x an y components (we’ll be using - two dimensional space, but everything here applies to 3D as well), but for this post we’re interested in something slightly different: We draw a line connecting the two objects. The component of in the direction of this line is called the normal component of relative velocity, while the component…