Synthetic hydroxyapatite (HAp) is an important material in biomedical engineering due to its excellent biocompatibility and bioactivity. Here we report dynamics of cetyltrimethylammonium bromide (CTAB) in HAp composite, prepared by co-precipitation method, as studied by quasielastic neutron scattering (QENS) technique. It is found that the observed dynamics involved two time scales associated with fast torsional motion and segmental motion of the CTAB monomers. In addition to segmental motion of the hydrogen atoms, few undergo torsional motion as well. Torsional dynamics was described by a 2-fold jump diffusion model. The segmental dynamics of CTAB has been described assumimg the hydrogen atoms undergoing diffusion inside a sphere of confined volume. While the diffusivity is found to increase with temperature, the spherical volumes within which the hydrogen atoms are undergoing diffusion remain almost unchanged.