As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes 10.5 y to travel between two planets that are not moving relative to each other. How long does the trip take as measured by
Someone on the spaceship?
A) 6.83 y
B) 2.79 y
C) 28.8 y
D) 39.5 y

Question

Quizplus · Accepted Answer

The time dilation formula, which is derived from the theory of relativity, is used to calculate the time experienced by someone moving at a significant fraction of the speed of light relative to an observer at rest. The formula is $ t' = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}} $, where $ t' $ is the time experienced by the moving observer, $ t $ is the time measured by the stationary observer, $ v $ is the velocity of the moving observer, and $ c $ is the speed of light. Plugging in the given values ($ t = 10.5 $ years, $ v = 0.9640c $), we find that the time experienced by someone on the spaceship is significantly less than the time measured by someone at rest due to the effects of time dilation, resulting in approximately 2.79 years.

As Measured in Earth's Rest Frame, a Spaceship Traveling at 0.9640c