You are a space traveler, moving at 0.60 c with respect to Earth, on your way to a star that is stationary relative to Earth. You measure the length of your trajectory to be 8.0 light-years (ly). Your friend makes the same journey at 0.80 c with respect to Earth. What does your friend measure the length of the trajectory to be? (Note: Light year is a unit of length)

In the realm of special relativity, the phenomenon of length contraction comes into play when considering measurements taken by observers in relative motion. Your friend, traveling at 0.80c, will measure the length of the trajectory to be shorter due to this effect. The length contraction formula is given by: \[ L = L_0 \sqrt{1 - \frac{v^2}{c^2}} \] where \( L_0 \) is the proper length (the length measured by an observer at rest with respect to the object being measured), \( v \) is the velocity of the moving observer, and \( c \) is the speed of light. Since the trajectory length you measured (proper length) is 8.0 ly, your friend’s journey at 0.80c will yield: \[ L = 8.0 \sqrt{1 - (0.80)^2} \approx 8.0 \sqrt{1 - 0.64} \approx 8.0 \sqrt{0.36} \approx 8.0 \times 0.6 = 4.8 \text{ ly} \] Thus, your friend measures the length of the trajectory to be approximately 4.8 light-years. Space travel truly brings out the wild and wacky effects of the universe!