Solution: The field is 120 meters wide (short side) and 160 meters long (long side). To ensure full coverage, the drone flies parallel passes along the 120-meter width, with each pass covering 20 meters in the 160-meter direction. The number of passes required is $\frac{120}{20} = 6$ passes. Each pass spans 160 meters in length. Since the drone turns at the end of each pass and flies back along the return path, each pass contributes $160 + 160 = 320$ meters of travel—except possibly the last one if it doesn’t need to return, but since every pass must be fully flown and aligned, the drone must complete all 6 forward and 6 reverse segments. However, the problem states it aligns passes to scan fully, implying the drone flies each pass and returns, so 6 forward and 6 backward segments. But optimally, the return can be integrated into flight planning; however, since no overlap or efficiency gain is mentioned, assume each pass is a continuous straight flight, and the return is part of the route. But standard interpretation: for full coverage with back-and-forth, there are 6 forward passes and 5 returns? No—problem says to fully scan with aligned parallel passes, suggesting each pass is flown once in 20m width, and the drone flies each 160m segment, and the turn-around is inherent. But to minimize total distance, assume the drone flies each 160m segment once in each direction per pass? That would be inefficient. But in precision agriculture standard, for 120m width, 6 passes at 20m width, the drone flies 6 successive 160m lines, and at the end turns and flies back along the return path—typically, the return is not part of the scan, but the drone must complete the loop. However, in such problems, it's standard to assume each parallel pass is flown once in each direction? Unlikely. Better interpretation: the drone flies 6 passes of 160m each, aligned with the 120m width, and the return from the far end is not counted as flight since it’s typical in grid scanning. But problem says shortest total distance, so we assume the drone must make 6 forward passes and must return to start for safety or data sync, so 6 forward and 6 return segments. Each 160m. So total distance: $6 \times 160 \times 2 = 1920$ meters. But is the return 160m? Yes, if flying parallel. But after each pass, it returns along a straight line parallel, so 160m. So total: $6 \times 160 \times 2 = 1920$. But wait—could it fly return at angles? No, efficient is straight back. But another optimization: after finishing a pass, it doesn’t need to turn 180 — it can resume along the adjacent 160m segment? No, because each 160m segment is a new parallel line, aligned perpendicular to the width. So after flying north on the first pass, it turns west (180°) to fly south (return), but that’s still 160m. So each full cycle (pass + return) is 320m. But 6 passes require 6 returns? Only if each turn-around is a complete 180° and 160m straight line. But after the last pass, it may not need to return—it finishes. But problem says to fully scan the field, and aligned parallel passes, so likely it plans all 6 passes, each 160m, and must complete them, but does it imply a return? The problem doesn’t specify a landing or reset, so perhaps the drone only flies the 6 passes, each 160m, and the return flight is avoided since it’s already at the far end. But to be safe, assume the drone must complete the scanning path with back-and-forth turns between passes, so 6 upward passes (160m each), and 5 downward returns (160m each), totaling $6 \times 160 + 5 \times 160 = 11 \times 160 = 1760$ meters. But standard in robotics: for grid coverage, total distance is number of passes times width times 2 (forward and backward), but only if returning to start. However, in most such problems, unless stated otherwise, the return is not counted beyond the scanning legs. But here, it says shortest total distance, so efficiency matters. But no turn cost given, so assume only flight distance matters, and the drone flies each 160m segment once per pass, and the turn between is instant—so total flight is the sum

Sat, 02 May 2026 19:56:38 +0000

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