Thus, the bird reaches its maximum altitude at $ \boxed{3} $ minutes after takeoff.Question: A precision agriculture drone programmer needs to optimize the route for monitoring crops across a rectangular field measuring 120 meters by 160 meters. The drone can fly in straight lines and covers a swath width of 20 meters per pass. To minimize turn-around time, it must align each parallel pass with the shorter side of the rectangle. What is the shortest total distance the drone must fly to fully sca

["Optimizing Drone Flight Path for Crop Monitoring: Calculating the Shortest Total Distance", "In precision agriculture, efficiency and accuracy determine the success of monitoring operations. For a rectangular field measuring 120 meters by 160 meters, ensuring complete coverage while minimizing wasted flight time is essential. This article explores the optimal flight path for a drone programmed to scan the entire field using parallel passes aligned with the shorter side.", "---", "### The Challenge: Covering a 120m × 160m Rectangular Field with 20m Scan Width", "The drone covers a swath width of 20 meters per straight pass, meaning each flight along a perpendicular line to the 120-meter side captures a 20-meter-wide strip across the 160-meter length. To fully scan the entire area without missing any spots, the drone must make multiple parallel passes spaced every 20 meters along the 160-meter dimension.", "---", "### Aligning Passes: Flying Across the Shorter Side", "To minimize turn maneuvers and optimize flight time, the drone aligns passes parallel to the 120-meter side—the shorter dimension—maximizing each pass’s effective coverage along the 160-meter length.", "---", "### Step 1: Determine Number of Passes", "- Field width (across shorter side): 120 meters\n- Swath width per pass: 20 meters\n- Number of passes required:\n [\n \frac{120\ \ ext{m}}{20\ \ ext{m/pass}} = 6\ \ ext{passes}\n ]\n The drone must make 6 passes, spaced 20 meters apart, to cover the full 120 meters.", "---", "### Step 2: Calculate Total Distance Per Pass and Total Flight Distance", "Each pass covers the full 160-meter length of the field. Since passes are parallel to the 120-meter side, each flight spans 160 meters. With 6 such passes:", "[\n\ ext{Total distance} = 6 \ imes 160\ \ ext{m} = 960\ \ ext{meters}\n]", "---", "### Step 3: Accounting for Turn Arounds", "While the drone may require brief turns at the start and end of each pass, the problem specifies optimizing for alignment with the shorter side, which reduces the need for sharp directional changes. However, transitions between parallel passes must be factored in.", "Because the passes are parallel and spaced exactly 20 meters apart (matching swath width), one straight transition between passes is sufficient—Ideally, after completing a pass, the drone aligns precisely for the next without extra turning— minimizing downtime.", "But to guarantee full coverage and precise alignment, we assume a simple on-off pattern: the drone completes each pass, turns 180° to reverse direction, flies the next, and repeats.", "Each turn involves flying back along some portion—but since we’re optimizing total path distance, reversals add no extra length; only the flight segments matter. The primary forward flight remains 6 × 160 = 960 meters.", "Thus, no additional distance is added by turns, and the total drone path equals the sum of all forward flights.", "---", "### Final Calculation", "[\n\ ext{Total optimized flight path} = 6 \ imes 160\ \ ext{m} = \boxed{960\ \ ext{meters}}\n]", "---", "### Conclusion", "By programming the drone to fly 6 parallel passes, each 160 meters long, aligned with the 120-meter side and utilizing a 20-meter swath, precision agriculture operators achieve full, efficient crop scanning in just 960 meters of total flight distance. This optimized route minimizes energy use, flight time, and operational wear—key factors in scalable, sustainable precision farming.", "For drone programmers, leveraging geometric alignment and swath efficiency transforms tedious patrol routes into intelligent, data-driven operations—proving that even simple field geometries unlock powerful automation gains."]