Final answer:
The question requires calculation of position vectors for two airplanes and the distance between them based on their altitudes, climb angles, and directions relative to a control tower.
Step-by-step explanation:
The question pertains to finding the position vectors of two airplanes, a Boeing 747 and a Douglas DC-3, relative to a control tower and determining the distance between them at a specific moment. To solve part (a), we would first need to represent the movement of the planes using vectors. For the Boeing 747, we would create a vector based on its altitude of 2500 m and its climb angle of 10° above the horizontal, moving 30° north of west. Similarly, for the Douglas DC-3, we would use its altitude of 3000 m and its climb angle of 5° above the horizontal, moving directly west.
For part (b), once the position vectors are established, we can apply vector subtraction to find the vector that represents the distance between the two planes. The magnitude of this resultant vector will give us the actual distance between the planes at the noted time.