How animals jump and land on a variety of surfaces is an ecologically important problem relevant to bioinspired robotics. We investigated this topic in the context of the jumping biomechanics of the planthopper Lycorma delicatula (the spotted lanternfly, SLF), an invasive insect in the US that jumps frequently for dispersal, locomotion, and predator evasion. High-speed video was used to analyze jumping by SLF nymphs from take-off to impact on compliant surfaces. These insects used rapid hindleg extensions to achieve high take-off speeds (2.7-3.4 m/s) and accelerations (800-1000 ms-2), with midair trajectories consistent with zero-drag ballistic motion without steering. Despite rotating rapidly (5-45 Hz) in the air about time-varying axes of rotation, they landed successfully in 58.9% of trials; they also attained the most successful impact orientation significantly more often than predicted by chance, consistent with their using attitude control. Notably, these insects were able to land successfully when impacting surfaces at all angles, pointing to the emerging importance of collisional recovery behaviors. To further understand their rotational dynamics, we created realistic 3D rendered models of SLFs and used them to compute their mechanical properties during jumping. Computer simulations based on these models and drag torques estimated from fits to tracked data successfully predicted several features of their measured rotational kinematics. This analysis showed that SLF nymphs are able to use posture changes and drag torques to control their angular velocity, and hence their orientation, thereby facilitating predominately successful landings when jumping.