Final answer:
The question appears to be incomplete and lacks crucial information needed to solve for the length of YZ. The provided information includes segment lengths but does not relate them in a way that allows for a solution.
Step-by-step explanation:
The question provided appears to be a mathematics problem related to geometry and possibly physics due to the mention of work (Joules). However, the question seems to have a typo or missing information, making it difficult to provide a complete answer. The given data includes two different segments, AD and DC, and corresponding lengths of 8 and 4 respectively, as well as a separate measure of WZ being 59. No mathematical relationship is provided to connect these measurements. Without additional context or relevant formulas, it is not possible to determine the length of YZ. Without clear instructions or more specific details related to the concepts like work-energy theorem or kinematics, an accurate and complete response cannot be given.