Final answer:
The change in velocity of a mirror when light reflects off of it involves applying principles from physics, such as momentum transfer and reflectivity, to calculate the force exerted and thus determine the change in velocity.
Step-by-step explanation:
The question involves calculating the change in velocity of a mirror due to the momentum imparted by photons from light reflecting off of it. When light reflects off a mirror, the change in momentum is twice that of the incident photon momentum. Since the intensity of the light is 789.0 W/m² and the duration of the light is 0.50 seconds, we can calculate the force exerted on the mirror by the photons and then use this to find the change in velocity. However, the angle of incidence is also important since it affects the component of the momentum that is transferred to the mirror in the direction normal to its surface.
If we take into account the reflectivity of the mirror, which is 98%, the total momentum transferred is slightly less than twice the incident photon momentum. Reflectivity indicates the fraction of light that is not absorbed, thus contributing to the momentum change. Since the mirror has a certain mass, the change in momentum results in a change in velocity, which can be computed using Newton's second law of motion and the principles of conservation of momentum.