So there are two vector problems that seem to be classic: someone trying to swim across a river that is flowing and an airplane flying with a given wind. For example, one might say a swimmer is swimming at 1m/s across a river with a .5m/s flow of water. Of course, you do the exercise to find you have to swim at an angle to reach the other side if you wanted to reach the other side without having drifted along the river bank. The other is the aircraft that travels at something like 200m/s North with a 10m/s crosswind and you find the "true speed" using vectors. I've had issues with how this problem is explained. With the river problem, it is more convincing that this is a realistic problem. However, I have never convinced myself of the airplane being realistic. If you are given the same problem with a very low density gas/atmosphere with said 10m/s crosswind, I can't imagine it would result in the same resultant velocity! The idea encompassing everything in this problem is the idea that an object "moves with its medium". Taking it to the extreme, imagine a real airplane (in size), a very low density gas with a very high average velocity of the particles, and I can't believe such a method is valid. So the question seems to be what conditions are necessary to facilitate such a simple analysis of velocity vectors? Hopefully I'm not the only person to think this strange... or maybe I'm missing something obvious.