Final answer:
The answer calculates the Boeing 747 and DC-3's position vectors using trigonometry and then finds the distance between the two planes by determining the difference between their vectors.
Step-by-step explanation:
The question involves determining the position vectors of two airplanes and the distance between them, which falls under the subject of physics, specifically kinematics and vector analysis. To solve this problem, we will use trigonometry and vector addition principles to calculate the position vectors and the distance between the two planes from a common reference point, the control tower.
(a) The Boeing 747's position vector can be resolved into its horizontal and vertical components using trigonometry based on its angle of ascent and compass heading. We will do the same for the DC-3, taking into account that it is cruising directly west.
(b) To find the distance between the planes, we must determine the difference between their position vectors, which requires finding the components of each vector and then applying the Pythagorean theorem to determine the distance.