Final answer:
The question asks about stopping a relativistic spaceship with light's drag force, which requires the use of relativistic dynamics, not simply dividing momenta. Relativistic effects like time dilation and length contraction, as well as the relativistic Doppler effect, must be considered in the calculations.
Step-by-step explanation:
The question involves the concept of relativistic velocity addition and the interaction between light and a moving spaceship. The momentum of the spaceship would not simply be divided by the momentum of the blueshifted light to find the time it takes for the spaceship to stop due to the drag force of light, as the scenario implies relativistic dynamics where Newtonian mechanics are no longer sufficient. Instead, one would need to consider the relativistic equations of motion, which take into account the factor γ (gamma), representing the relativistic factor for time dilation and length contraction.
When the spaceship is travelling at relativistic speeds, classical concepts like momentum and force need to be reconsidered using the principles of special relativity. The process of slowing down would involve complex calculations including the spaceship's mass, its velocity, the energy and momentum of the photons of light, and how these quantities transform between different reference frames. To determine the time it would take for the spaceship to stop under the influence of light's drag force, one would have to solve the relativistic momentum equations, which may also involve the relativistic Doppler effect to understand how light's interaction with the spaceship changes due to the relative motion at high speeds.