The use of unmanned aerial vehicles (UAVs) acting as flying base stations (FlyBSs) is considered as an effective tool to improve performance of the mobile networks. Nevertheless, such potential improvement requires an efficient positioning of the FlyBS. In this paper, we maximize the sum downlink capacity of the mobile Internet of Things devices (IoTD) served by the FlyBSs while a minimum required capacity to every device is guaranteed. To this end, we propose a geometrical approach allowing to derive the 3D positions of the FlyBS over time as the IoTDs move and we determine the transmission power allocation for the IoTDs. The problem is formulated and solved under practical constraints on the FlyBS's transmission and propulsion power consumption as well as on flying speed. The proposed solution is of a low complexity and increases the sum capacity by 15%-46% comparing to state-of-the-art works.