Final answer:
Maximum hip extension occurs during the Terminal Stance phase of the gait cycle when the leg is behind the body and the hip extends maximally to maintain balance and propel forward motion.
Step-by-step explanation:
Maximum hip extension occurs during the gait cycle at the phase identified as Terminal Stance. This is the moment when the leg is behind the body and the hip is in its greatest extension before the leg moves forward for the next step. During this phase, the body's weight moves over the stationary foot on the ground, requiring the hip to extend to maintain balance and forward motion.