We consider a novel hybrid active-passive reconfigurable intelligent surface (RIS)-assisted unmanned aerial vehicle (UAV) air-ground communications system. Unlike the conventional passive RIS, the hybrid RIS is equipped with a few active elements to not only reflect but also amplify the incident signals for significant performance improvement. Towards a fairness design, our goal is to maximize the minimum rate among users through jointly optimizing the location and power allocation of the UAV and the RIS reflecting/amplifying coefficients. The formulated optimization problem is nonconvex and challenging, which is efficiently solved via block coordinate descend and successive convex approximation. Our numerical results show that a hybrid RIS requires only 4 active elements and a power budget of 0 dBm to achieve an improvement of 52.08% in the minimum rate, while that achieved by a conventional passive RIS with the same total number of elements is only 18.06%.