Falls are dangerous for the elderly, often causing serious injuries especially when the fallen person stays on the ground for a long time without assistance. This paper extends our previous work on the development of a Fall Detection System (FDS) using an inertial measurement unit worn at the waist. Data come from SisFall, a publicly available dataset containing records of Activities of Daily Living and falls. We first applied a preprocessing and a feature extraction stage before using five Machine Learning algorithms, allowing us to compare them. Ensemble learning algorithms such as Random Forest and Gradient Boosting have the best performance, with a Sensitivity and Specificity both close to 99%. Our contribution is: a multi-class classification approach for fall detection combined with a study of the effect of the sensors’ sampling rate on the performance of the FDS. Our multi-class classification approach splits the fall into three phases: pre-fall, impact, post-fall. The extension to a multi-class problem is not trivial and we present a well-performing solution. We experimented sampling rates between 1 and 200 Hz. The results show that, while high sampling rates tend to improve performance, a sampling rate of 50 Hz is generally sufficient for an accurate detection.