A particle is thrown tangentially on a surface. It is shown that for some surfaces and for special initial velocities the thrown particle immediately leaves the surface, and for special conditions it never leaves the surface. The conditions for leaving the surface are investigated. The problem is studied for a surface with the cross-section y = f(x). The surfaces with the equations f(x) = -[alpha]x[superscript k] ([alpha], k greater than 0) are considered in more detail. Finally, the effect of friction is also considered. (Contains 4 figures.)