Serway & Jewett — Vectors: Problem 42

You are working as an assistant to an air-traffic controller at the local airport, from which small airplanes take off and land. Your job is to make sure that airplanes are not closer to each other than a minimum safe separation distance of 2.00 km. You observe two small aircraft on your radar screen, out over the ocean surface. The first is at altitude 800 m above the surface, horizontal distance 19.2 km, and \(25.0^\circ\) south of west. The second aircraft is at altitude 1 100 m, horizontal distance 17.6 km, and \(20.0^\circ\) south of west. Your supervisor is concerned that the two aircraft are too close together and asks for a separation distance for the two airplanes. (Place the \(x\) axis west, the \(y\) axis south, and the \(z\) axis vertical.)