A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on board the spaceship?
A) 5.38 y
B) 3.23 y
C) 5.15 y
D) 4.40 y

Question

Quizplus · Accepted Answer

The time elapsed on a clock on board the spaceship can be calculated using the time dilation formula in special relativity, $ t' = \frac{t}{\sqrt{1 - v^2/c^2}} $, where $ t $ is the time in the Earth frame, $ v $ is the velocity of the spaceship, and $ c $ is the speed of light. First, calculate the time in the Earth frame: $ t = \frac{distance}{speed} = \frac{4.30 \, \text{light-years}}{0.800c} = 5.375 \, \text{years} $. Then, apply the time dilation formula: $ t' = \frac{5.375}{\sqrt{1 - (0.800)^2}} \approx 3.23 \, \text{years} $.

A Spaceship with a Constant Speed of 0