Following our recent system-bath modeling of the interaction between a hydrogen atom and a graphene surface (M Bonfanti et al., XXX), we present the results of converged quantum scattering calculations on the activated sticking dynamics. The focus of this study is the collinear scattering on a surface at zero temperature, which is treated with high-dimensional wavepacket propagations with the multi-configuration time-dependent Hartree method. At low collision energies barrier-crossing dominates the sticking and any projectile that overcomes the barrier gets trapped in the chemisorption well. However, at high collision energies energy transfer to the surface is a limiting factor, and fast H atoms hardly dissipate their excess energy and stick on the surface. As a consequence, the sticking coefficient is maximum ($0:65) at an energy which is about one and half larger than the barrier height. Comparison of the results with classical and quasi-classical calculations shows that quantum fluctuations of the lattice play a primary role in the dynamics. A simple impulsive model describing the collision of a classical projectile with a quantum surface is developed which reproduces the quantum results remarkably well for all but the lowest energies, thereby capturing the essential physics of the activated sticking dynamics investigated