Under the hypothesis that Mg ii absorbers found near the minor axis of a disc galaxy originate in the cool phase of supergalactic winds, we carry out a study to constrain the properties of large-scale galactic outflows at redshift zgal ≳ 0.5 based on the observed relative motions of individual absorbing clouds with respect to the positions and orientations of the absorbing galaxies. We identify in the literature four highly inclined disc galaxies located within 50 kpc and with the minor axis oriented within 45° of a background quasi-stellar object (QSO) sightline. Deep Hubble Space Telescope images of the galaxies are available for accurate characterizations of the optical morphologies of the galaxies. High-quality echelle spectra of the QSO members are also available in public archives for resolving the velocity field of individual absorption clumps. Three galaxies in our sample are located at ρ = 8–34 kpc and exhibit strong associated Mg ii absorption feature with Å. One galaxy, located at an impact parameters ρ = 48 kpc, dose not show an associated Mg ii absorber to a 3σ limit of Å. Combining known morphological parameters of the galaxies such as the inclination and orientation angles of the star-forming discs, and resolved absorption profiles of the associated absorbers at ρ < 35 kpc away, we explore the allowed parameter space for the opening angle θ0 and the velocity field of large-scale galactic outflows as a function of z-height, v(z). We find that the observed absorption profiles of the Mg ii doublets and their associated Fe ii series are compatible with the absorbing gas being either accelerated or decelerated, depending on θ0, though accelerated outflows are a valid characterization only for a narrow range of θ0. Under an acceleration scenario, we compare the derived v(z) with predictions from Murray et al. and find that if the gas is being accelerated by the radiation and ram pressure forces from super star clusters, then the efficiency of thermal energy input from a supernova explosion is ε ≲ 0.01. In addition, we adopt a power-law function from Steidel et al. for characterizing the accelerated outflows as a function of z-height, a(z) ∝ z−α. We find a steep slope of α ≈ 3 for a launch radius of zmin = 1 kpc. A shallower slope of α ≈ 1.5 would increase zmin to beyond 4 kpc. We discuss the implications of these parameter constraints.