Elastic scattering cross sections are measured for lithium atoms colliding with rare gas atoms and SF6 molecules at tunable relative velocities down to ~50 m/s. Our scattering apparatus combines a velocity-tunable molecular beam with a magneto-optic trap that provides an ultracold cloud of lithium atoms as a scattering target. Comparison with theory reveals the quantum nature of the collision dynamics in the studied regime, including both rainbows as well as orbiting resonances.