Question

as measured in earth's rest frame, a spaceship traveling 0.964 c at takes 11.2 years to travel between planets. how long does the trip take as measured by someone on the spaceship? group of answer choices 2.98 years 7.28 years 42.1 years 30.7 years

Answer 1

To determine the duration of the trip as measured by someone on the spaceship, we can use the time dilation formula from special relativity:

Δt' = Δt / √(1 - (v^2/c^2))

Where:
Δt' is the time dilation experienced by the traveler on the spaceship,
Δt is the time measured in the Earth's rest frame (11.2 years in this case),
v is the velocity of the spaceship (0.964c, where c is the speed of light),
and c is the speed of light.

Plugging in the values:

Δt' = 11.2 / √(1 - (0.964^2))
Δt' = 11.2 / √(1 - 0.929296)
Δt' = 11.2 / √(0.070704)
Δt' = 11.2 / 0.265932
Δt' = 42.1 years

Therefore, the trip takes approximately 42.1 years as measured by someone on the spaceship.