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

Question

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

Quizplus · Accepted Answer

We can use the formula for time dilation to find the spaceship's speed. In the Earth's rest frame, the spaceship's trip took 10.0 years. In the spaceship's frame, the trip took 11 years. We can plug these values into the time dilation equation:

t_0 = t_f / sqrt(1 - v^2/c^2)

where t_0 is the time in the Earth's rest frame, t_f is the time in the spaceship's frame, v is the spaceship's speed relative to Earth, and c is the speed of light.

Rearranging this equation and squaring both sides, we get:

v^2/c^2 = 1 - (t_f/t_0)^2

Plugging in the values from the problem, we get:

v^2/c^2 = 1 - (11/10)^2 = 0.19

Taking the square root of both sides and multiplying by c, we get:

v = 0.816 c

So the answer is A) 0.816 c.

Someone in Earth's Rest Frame Says That a Spaceship's Trip