The impact of high-speed jets -- dynamic pressure enhancements in the magnetosheath -- on the Earths magnetopause has been observed to trigger local magnetic reconnection. We perform a three-dimensional hybrid simulation to study the magnetosheath and magnetopause under turbulent conditions using a quasi-radial southward interplanetary magnetic field (IMF). In contrast to quasi-steady reconnection with a strong southward IMF, we show that after the impact of a jet on the magnetopause, the magnetopause moves inwards, the current sheet is compressed and intensified and signatures of local magnetic reconnection are observed, showing similarities to spacecraft measurements