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NASA's Transiting Exoplanet Survey Satellite (TESS) mission, has been uncovering a growing number of exoplanets orbiting nearby, bright stars. Most exoplanets that have been discovered by TESS orbit narrow-line, slow-rotating stars, facilitating the confirmation and mass determination of these worlds. We present the discovery of a hot Jupiter orbiting a rapidly rotating ($v\sin{(i)}= 35.1\pm1.0$km/s) early F3V-dwarf, HD115447 (TOI-778). The transit signal taken from Sectors 10 and 37 of TESS's initial detection of the exoplanet is combined with follow-up ground-based photometry and velocity measurements taken from Minerva-Australis, TRES, CORALIE and CHIRON to confirm and characterise TOI-778b. A joint analysis of the light curves and the radial velocity measurements yield a mass, radius, and orbital period for TOI-778b of $2.76^{+0.24}_{-0.23}$Mjup, $1.370\pm0.043$Rjup and $\sim4.63$ days, respectively. The planet orbits a bright ($V = 9.1$mag) F3-dwarf with $M=1.40\pm0.05$Msun, $R=1.70\pm0.05$Rsun, and $\log g=4.05\pm0.17$. We observed a spectroscopic transit of TOI-778b, which allowed us to derive a sky-projected spin-orbit angle of $18^{\circ}\pm11^{\circ}$, consistent with an aligned planetary system. This discovery demonstrates the capability of smaller aperture telescopes such as Minerva-Australis to detect the radial velocity signals produced by planets orbiting broad-line, rapidly rotating stars., Comment: 18 pages, 9 figures, and 4 tables. Submitted to the Astronomical Journal