Someone in Earth's rest frame says that a spaceship's trip between two planets took $10.0 \mathrm { y }$, while an astronaut on the space ship says that the trip took $5.78 \mathrm { y }$. What is the speed of the spaceship, assuming the planets are at essentially at rest?
A) $0.816 \mathrm { c }$
B) $0.384 \mathrm { c }$
C) $0.735 \mathrm { c }$
D) $0.975 \mathrm { c }$

Question

Quizplus · Accepted Answer

The time dilation formula is $\Delta t' = \Delta t / \sqrt{1 - v^2/c^2}$, where $\Delta t'$ is the time interval in the moving frame (5.78 years), $\Delta t$ is the time interval in the rest frame (10.0 years), and $v$ is the velocity of the moving frame. Solving for $v/c$ gives $v/c = \sqrt{1 - (\Delta t'/\Delta t)^2} = \sqrt{1 - (5.78/10)^2} = 0.816$, which means the speed of the spaceship is $0.816c$.

Someone in Earth's Rest Frame Says That a Spaceship's Trip 10.0y10.0 \mathrm { y }10.0y

Someone in Earth's Rest Frame Says That a Spaceship's Trip $10.0 \mathrm { y }$