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?

Question

Quizplus · Accepted Answer

This is a problem involving time dilation, which is a consequence of special relativity. According to special relativity, time slows down for objects that are moving relative to an observer. The formula for time dilation is given by:

t' = t / sqrt(1 - v^2/c^2)

where t is the time interval in the rest frame (i.e., the time measured by an observer who is not moving), t' is the time interval in the moving frame (i.e., the time measured by an observer who is moving), v is the speed of the moving frame relative to the rest frame, and c is the speed of light.

In this problem, the spaceship is moving at 0.9640c relative to the rest frame (i.e., Earth), and the time interval in the rest frame is 10.5 years. Therefore, we can use the formula to find the time interval in the moving frame:

t' = 10.5 / sqrt(1 - 0.9640^2) = 2.79 years

Therefore, the answer is A.

As Measured in Earth's Rest Frame,a Spaceship Traveling at 0 10.5y10.5 \mathrm { y }10.5y

As Measured in Earth's Rest Frame,a Spaceship Traveling at 0 $10.5 \mathrm { y }$