Application Research of Physical Model Based on Differential Equation Theory in Salvaging Dropped Items

Abstract

Incidents of items accidentally falling into water are common in daily life, especially during travel, where important items such as ID cards and mobile phones fall into water. This article uses the items falling into the West Lake and the Beijing-Hangzhou Grand Canal as examples. By utilizing the theory of differential equations advanced mathematics, a physical model is established. The model takes into account the impact of water flow speed, direction, wind speed, and other factors on the final point of the item. It provides a detailed simulation of the item's descent process in the water and analyzes the trajectory of the item's movement in the water. Python for numerical simulation, the recommended search radius for a mobile phone falling into the West Lake is obtained as 0.00042m, while a mobile phone falling into the Grand Canal, the recommended search radius is 0.18m, Similar analysis of ID search radius in West Lake and Grand Canal areas, These results provide theoretical support and scientific basis for actual retrieval work.