2.3 Exercise 18

In the control tower at a regional airport, an air traffic controller monitors two aircraft that travel in straight paths directly away from the control tower. One plane is a cargo carrier Boeing 747 climbing at $10 °$ above the horizontal, and moving $30 °$ north of west. At some moment in time, the controller notes that the Boeing is at an altitude of 2500 m and the DC-3 is at an altitude of 3000 m. The other plane is a Douglas DC-3 climbing at $5 °$ above the horizontal, and cruising directly west. (a) Find the position vectors of the planes relative to the control tower at this time. (b) What is the distance between the planes at this time?