Question

An astronaut on a fast-moving spaceship appears to age only $1$ year to an outside observer, even though the person travels for $5$ years from the observer's perspective. The astronaut travels a distance of X during this time, from the observer's perspective.
Which of the following is true from the astronaut's perspective?

• A. The astronaut ages $5$ years during the trip
• B. The distance the astronaut travels is X
• C. The distance the astronaut travels is greater than X
• D. The distance the astronaut travels is less than X
• E. The astronaut ages more than $5$ years during the trip

Answer 1

The correct option is D The distance the astronaut travels is less than X

Time of journey from the person's perspective, $t=5$ year

Thus distance traveled from the person's perspective, $X=vt=5v$

Time of journey from the astronaut's perspective, $t^{\prime }=1$ year

Thus distance traveled from the astronaut's perspective, $d^{\prime }=v{t}^{\prime }=v$ $⟹$ $d^{\prime }<X$