When a flashlight is turned on inside a spaceship traveling at 7.52 x 10^7 m/s, the speed of the light ray relative to the spaceship is always the speed of light, approximately 299,792,458 m/s. According to the principles of Special Relativity, the speed of light remains constant regardless of the observer's frame of reference. Therefore, while the light travels at the speed of light relative to the spaceship, its speed relative to Earth is calculated using the relativistic addition of velocities, resulting in a speed still close to the speed of light. This illustrates the fundamental concept that light's speed is invariant in all inertial frames. Understanding these principles is crucial for solving problems in relativistic physics.