Astronaut Rachel leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rachel's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). According to Rachel, how long does the trip take?
A) 14.4 years
B) 15.0 years
C) 10.8 years
D) 4.20 years
E) 22.7 years

Question

Quizplus · Accepted Answer

According to special relativity, time dilation occurs for objects moving at high speeds relative to each other. This means that time appears to pass more slowly for Rachel on the moving spaceship, as observed by the stationary observer on Earth.

Using the formula for time dilation:

t' = t / sqrt(1 - v^2/c^2)

where t is the time interval on Earth, t' is the time interval on the spaceship, v is the velocity of the spaceship relative to Earth (0.960c), and c is the speed of light.

Substituting the given values, we get:

t' = 14.4 years / sqrt(1 - 0.960^2) = 4.20 years

Therefore, according to Rachel on the spaceship, the trip takes 4.20 years. So, the correct answer is option D.

Astronaut Rachel Leaves Earth in a Spaceship at a Speed