Astronaut Rachel leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth.Rachel's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year).According to Rachel,how long does the trip take?
A)14 years
B)15 years
C)11 years
D)4.2 years
E)23 years

Question

Quizplus · Accepted Answer

According to special relativity, time dilation occurs when an object is moving relative to an observer. As Rachel is moving at a speed of 0.960c relative to an observer on Earth, time appears to slow down for Rachel from the perspective of the observer on Earth. To calculate the time taken for Rachel's journey, we need to use the time dilation formula:

t = t0 / sqrt(1 - v^2/c^2)

where
t0 = time taken for the journey from Rachel's perspective
v = velocity of Rachel's spaceship = 0.960c
c = speed of light
t = time taken for the journey from the observer's perspective

Plugging in the values, we get:

t = 14.4 / sqrt(1 - 0.960^2) = 4.2 years (approx)

Therefore, the best choice is D (4.2 years).

Astronaut Rachel Leaves Earth in a Spaceship at a Speed