As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes $10.5 \mathrm { y }$ 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) 2.79 y
B) 6.83 y
C) 39.5 y
D) 28.8 y

Question

Quizplus · Accepted Answer

Explanation:The time dilation formula is:$$t' = \frac{t}{\gamma}$$where $t'$ is the time measured in the moving frame, $t$ is the time measured in the stationary frame, and $\gamma$ is the Lorentz factor:$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$Plugging in the given values, we get:$$\gamma = \frac{1}{\sqrt{1 - 0.9640^2}} = 5.029$$$$t' = \frac{10.5 \mathrm { y }}{5.029} = 2.79 \mathrm { y }$$

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