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)2.58 light-years
B)3.52 light-years
C)4.12 light-years
D)4.30 light-years

Question

Quizplus · Accepted Answer

The distance measured by a passenger on the ship is shorter due to length contraction, a phenomenon of 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 numbers, $L = 4.30\sqrt{1 - (0.800)^2} = 4.30\sqrt{1 - 0.64} = 4.30\sqrt{0.36} = 4.30 \times 0.6 = 2.58$ light-years.

A Spaceship with a Constant Velocity of 0