A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth. What distance does the space ship travel as measured by a passenger on
The ship?
A) $4.30$ light-years
B) $2.58$ light-years
C) $3.52$ light-years
D) $4.12$ light-years

Question

A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth. What distance does the space ship travel as measured by a passenger on
The ship? 
A) $4.30$ light-years
B) $2.58$ light-years
C) $3.52$ light-years
D) $4.12$ light-years

Quizplus · Accepted Answer

The distance traveled as measured by a passenger on the ship is shorter than the distance measured from Earth due to length contraction, a phenomenon predicted by special relativity. The formula for length contraction is $L = L_0\sqrt{1-v^2/c^2}$, where $L_0$ is the rest length (4.30 light-years), $v$ is the velocity of the ship (0.800c), and $c$ is the speed of light. Plugging in the values, we get $L = 4.30\sqrt{1-0.800^2} = 4.30\sqrt{1-0.64} = 4.30\sqrt{0.36} = 4.30 \times 0.6 = 2.58$ light-years.

A Spaceship with a Constant Velocity of 0 4.304.304.30 Light-Years B) 2.582.582.58

A Spaceship with a Constant Velocity of 0 $4.30$ Light-Years
B) $2.58$