While riding my bike today, I had an idea for an AP physics/calculus question. Suppose two bicyclists pass one another going in opposite directions on a long, straight road. Given a fixed maximum power output P1, P2 of each cyclist, respectively, and assuming that the road is long enough that each cyclist can reach his/her "terminal velocity" for that road's slope, consider the maximum closing speed |v1-v2| of the two cyclists. Now consider how this maximum varies with the slope of the long, straight road. As we vary the slope of the road, is there a single maximum closing speed? Or are there several different slopes with relative maximal closing speeds? Normally the power is proportional to the cube of the velocity: https://en.wikipedia.org/wiki/Drag_%28physics%29