The problem of relativistic physics is solved to find the initial angle of a maximum range throw in a uniform force field with a fixed initial velocity. Two physically different formulations are considered: the relativistic motion of a charged particle in a uniform electric field, and the motion of a particle in a uniform gravitational field in accordance with the general theory of relativity. It is shown that the maximum range throw angle in both cases monotonously depends on the initial velocity, increasing from 45 degrees for velocities small compared to the speed of light to approximately 56.5 degrees for motion in a uniform electric field and to 90 degrees for motion in a uniform gravitational field, at velocities approaching the speed of light.