Length contraction: An astronaut leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. The astronaut's destination is a star system 14.4 light-years away. (One light-year is the distance light travels in one year.) According to the astronaut, how long does the trip take?
A) 14.4 y
B) 22.7 y
C) 9.34 y
D) 15.0 y
E) 4.20 y

Question

Quizplus · Accepted Answer

To find the time it takes according to the astronaut, we use the formula for length contraction: $L = L_0\sqrt{1 - v^2/c^2}$, where $L_0$ is the rest length (14.4 light-years), $v$ is the velocity of the spaceship (0.960c), and $c$ is the speed of light. Plugging in the values, we get the contracted length $L$. The time it takes according to the astronaut is then $L/v$. After calculating, we find that the time is approximately 4.20 years, which corresponds to choice E.

Length Contraction: an Astronaut Leaves Earth in a Spaceship at a Speed