(Originais Teachy 2023) - Question Easy of Physics

In a physics experiment, a group of students set out to empirically verify the time dilation predicted by Einstein's Special Theory of Relativity. They use an extremely precise clock capable of measuring time with nanosecond precision. They set up an experiment to measure the time it takes for a beam of light to travel a distance of 300 million meters at rest and aboard a hypothetical spaceship traveling at a constant speed of 0.8c, where c is the speed of light in a vacuum (c = 3 x 10^8 m/s). Considering the Lorentz factor (γ) as γ = 1/sqrt(1 - (v^2/c^2)), where v is the spaceship's velocity: (a) Calculate the time measured for the beam of light to travel the distance at rest and compare it with the time measured aboard the spaceship. (b) Explain how time dilation manifests in this experiment and the importance of this phenomenon for understanding the universe.