This paper studies an unmanned aerial vehicle (UAV)-enabled wireless sensor network, in which one UAV flies in the sky to collect the data transmitted from a set of ground nodes (GNs) via distributed beamforming. We consider two scenarios with delay-tolerant and delay-sensitive applications, in which the GNs send the common/shared messages to the UAV via adaptive- and fixed-rate transmissions, respectively. For the two scenarios, we aim to maximize the average data-rate throughput and minimize the transmission outage probability, respectively, by jointly optimizing the UAV's trajectory design and the GNs' transmit power allocation over time, subject to the UAV's flight speed constraints and the GNs' individual average power constraints. However, the two formulated problems are both non-convex and thus generally difficult to be optimally solved. To tackle this issue, we first consider the relaxed problems in the ideal case with the UAV's flight speed constraints ignored, for which the well-structured optimal solutions are obtained to reveal the fundamental performance upper bounds. It is shown that for the two approximate problems, the optimal trajectory solutions have the same multi-location-hovering structure, but with different optimal power allocation strategies. Next, for the general problems with the UAV's flight speed constraints considered, we propose efficient algorithms to obtain high-quality solutions by using the techniques from convex optimization and approximation. Finally, numerical results show that our proposed designs significantly outperform other benchmark schemes, in terms of the achieved data-rate throughput and outage probability under the two scenarios. It is also observed that when the mission period becomes sufficiently long, our proposed designs approach the performance upper bounds when the UAV's flight speed constraints are ignored.