Employing unmanned aerial vehicles (UAVs) for data collection is crucial in facilitating autonomous monitoring applications within wireless sensor networks (WSNs). To enable sustainable WSNs, wireless powering of ground nodes (GNs) from a flying UAV is a promising technique. However, to maximize utility, we need to smartly allocate the limited resources of UAVs. To this end, we propose jointly optimizing the UAV’s trajectory and time allocation per GN to reduce operation time. We first formulate a non-convex optimization problem for data collection that minimizes operation time while satisfying the sum throughput and time constraint. Thereafter, we develop a methodology that decouples the original problem into two sub-problems: time allocation and trajectory planning. Here, the former is solved in semi-closed form, while a genetic algorithm is employed to solve the latter. Simulations confirm the efficiency of our proposed model and unveil an up to 30% improvement in operation time compared to the existing benchmarks.