Differential cross sections and analysing powers for the reaction 9Be(p →, p′) have been measured at incident proton energies of 54.7 and 74.7 MeV. The new data, supplemented by existing data in the energy range from 30 to 220 MeV, has been subjected to various analyses with the aim of obtaining optical potentials to calculate final-state interaction effects in proton-knockout reactions. A conventional optical model analysis fails to give a description that is in simultaneous agreement with all elastic scattering data. A considerable improvement is obtained by including the quadrupole contribution to elastic scattering, both with phenomenological and microscopic potentials. Finally, the influences of the various reaction mechanisms and of the differences between the derived potentials are studied when applied to (e,e′p) and (γ,p) calculations in the distorted wave impulse approximation.