We study cold heteronuclear atom ion collisions by immersing a trapped single ion into an ultracold atomic cloud. Using ultracold atoms as reaction targets, our measurement is sensitive to elastic collisions with extremely small energy transfer. The observed energy-dependent elastic atom-ion scattering rate deviates significantly from the prediction of Langevin but is in full agreement with the quantum mechanical cross section. Additionally, we characterize inelastic collisions leading to chemical reactions at the single particle level and measure the energy-dependent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and non-radiative charge exchange processes.