The integration of unmanned aerial vehicles (UAVs) into wireless communication systems has emerged as a transformative approach, promising cost-efficient connectivity. This paper addresses the optimization of the dynamic time-splitting ratio and flight trajectory for a communication system linking a ground base station to the UAV equipped with backscatter devices (referred to as UB), and from UB to an end user. Given the inherent non-convexity of the problem, we develop two meta-heuristic-based approaches inspired by genetic algorithm and particle swarm optimization to enhance the total achievable rate while reducing computational complexity. Numerical results demonstrate the effectiveness of these meta-heuristic solutions, showcasing significant improvements in the achievable rate and computation time compared to existing benchmarks.