We consider the benchmark configuration of a falling elastic ball within a viscous fluid and its rebound after contact with a lower wall. Different contact models are discussed and a variational fully Eulerian formulation is introduced for the fluid-structure-contact interaction problem. Both the fluid-structure coupling conditions as well as the contact condition are incorporated weakly and fully implicitly into the variational formulation by using Nitsche's method. For discretisation, we consider on one hand a fitted finite element discretisation based on the locally modified finite element method, where the mesh is updated (only) locally in each time step to resolve the interface. On the other hand, we consider a recently developed unfitted cut finite element method, where the mesh stays identical for all time steps and ghost penalty stabilisations are applied in both fluid and solid subproblems. The resulting methods are compared to alternative approaches by means of the above mentioned benchmark configuration.