We study the dynamics of plankton in the wake of a jellyfish. Using an analytical approach, we derive a reduced-order equation that governs the prey motion which is modeled as neutrally-buoyant inertial particle. This modified equation takes into account both the effects of prey inertia and self-propulsion and enables us to calculate both the attracting and repelling Lagrangian coherent structures for the prey motion. For the case of zero self-propulsion, it is simplified to the equation of motion for infinitesimal fluid particles. Additionally, we determine the critical size of prey over which instabilities on its motion occur resulting in different dynamics from those predicted by the reduced-order equation even for the case of zero self-propulsion. We illustrate our theoretical findings through an experimentally measured velocity field of a jellyfish. Using the inertial equation, we calculate the Lagrangian coherent structures that characterize prey motion as well as the instability regions over which larger prey will have different dynamics even for the case of zero self-propulsion.