The sticking of one hydrogen atom chemisorbed on the (0001) graphite surface is investigated using a mixed classical-quantum method. The phonon modes of the system in the collinear scattering approach are included in the dynamics calculations. The vibrational degrees of freedom of the surface (phonons) are treated classically, while the H-surface motion is treated using a one-dimensional quantum wave packet propagation method. The sticking probabilities are calculated and the individual contributions of the phonon bands to the collision dynamics are analyzed for surface temperatures of 10, 150, and 300 K and hydrogen kinetic energies ranging from 0.13 to 1.08 eV. An analytical form of the sticking probability as a function of the surface temperature is also proposed.