As organisms swim in their natural environment, they are constantly striving to successfully forage, escape from predation, and search for mates to reproduce. At some stage in their life cycle, most organisms in the ocean have operated in environments where the Reynolds number (Re) is small and have developed strategies and behaviors to overcome the effects of viscosity. Relatively little is known about these animal-fluid interactions at relatively small (Re > 1), viscous size scales. We combine high-speed kinematic and velocity field measurements of 1-mm velar-diameter, jet-propelled medusae, Sarsia tubulosa, and apply rigorous criteria to identify an analytical model that best describes the hydrodynamic signals created during swimming. We found that the hydrodynamic signature of a jet-propelled medusa at relatively small size scales is best described by an impulsive Stokeslet, which has important ecological implications for the ambush-feeding predator.