Motion of a Relativistic Particle Acted Upon by a Constant Force and a Uniform Gravitational Field, I. Richard Lapidus, Am. J. Phys., July 1972
The complete two-dimensional solutions for the relativistic motion of a particle acted upon by a constant force and a uniform gravitational field are obtained. The gravitational force is velocity dependant as a consequence of the equivalence of inertial and gravitational mass. The solution for the special case of one-dimensional vertical motion is also obtained.