Analyzing a Drone’s Flight Path

You’re programming a drone for an aerial photography project at a local park. The drone’s flight path needs to be carefully planned to capture footage while avoiding obstacles. The drone’s position at any time [latex]t[/latex] (measured in seconds) can be described using vector-valued functions, where distances are measured in meters. Your task is to analyze different flight paths by evaluating the vector functions, understanding their domains, identifying the shapes of the paths, and verifying that the paths are safe by checking limits at critical points.