Final answer:
The three horizontal ropes are used to pull the SUV out of the mud, harnessing tension created by a sideways force to produce sufficient pulling force.
Step-by-step explanation:
The purpose of using three horizontal ropes to extricate an SUV stuck in the mud is to pull the SUV out of the mud. When force is applied to the center of these ropes, it creates tension along the ropes, providing the necessary force to move the vehicle. The scenario described is based on Newton's laws of motion and the principle that applying a sideways force at the center of a taut rope or chain can generate a large amount of force at the ends, beneficial for situations requiring towing or pulling. Using multiple ropes increases the amount of force that can be applied simultaneously, making the extrication process more effective.