As measured in Earth's rest frame, a spaceship traveling at 0.964c takes 11.2 y to travel between planets. How long does the trip take as measured by someone on the spaceship?
A) 2.98 y
B) 7.28 y
C) 42.1 y
D) 30.7 y

Question

Quizplus · Accepted Answer

Explanation:The time dilation formula is:$$t' = t/\gamma$$where:$$t'$$ is the time measured in the spaceship's frame of reference$$t$$ is the time measured in Earth's frame of reference$$\gamma$$ is the Lorentz factor, which is given by:$$\gamma = 1/\sqrt{1 - v^2/c^2}$$where:$$v$$ is the velocity of the spaceship$$c$$ is the speed of lightPlugging in the given values, we get:$$\gamma = 1/\sqrt{1 - 0.964^2} = 3.2$$$$t' = 11.2 y/3.2 = 2.98 y$$Therefore, the trip takes 2.98 years as measured by someone on the spaceship.

As Measured in Earth's Rest Frame, a Spaceship Traveling at 0.964c