600 meters 84 meters Change in starship's length when moving at 99% of light's speed when viewed by an observer Starship at rest a. Find lim Ra. b. If you are traveling in a starship at velocities approaching the speed of light, what does the limit in part (a) indicate about your aging rate relative to a friend on Earth? c. Explain why a left-hand limit is used in part (a).

Question

In Albert Einstein’s special theory of relativity, time slows down and length in the direction of motion decreases from the point of view of an observer watching an object moving at velocities approaching the speed of light. (The speed of light is approximately 186,000 miles per second. At this speed, a beam of light can travel around the world about seven times in a single second). The formula Ra = Rf √(1 -v2/c2) expresses the aging rate of an astronaut, Ra, relative to the aging rate of a friend on Earth, Rf, where v is the astronaut’s velocity and c is the speed of light.

600
meters
84
meters
Change in starship's length
when moving at 99% of light's speed
when viewed by an observer
Starship at rest

Image Transcription

600 meters 84 meters Change in starship's length when moving at 99% of light's speed when viewed by an observer Starship at rest

a. Find lim Ra.
b. If you are traveling in a starship at velocities approaching
the speed of light, what does the limit in part (a) indicate
about your aging rate relative to a friend on Earth?
c. Explain why a left-hand limit is used in part (a).

Image Transcription

a. Find lim Ra. b. If you are traveling in a starship at velocities approaching the speed of light, what does the limit in part (a) indicate about your aging rate relative to a friend on Earth? c. Explain why a left-hand limit is used in part (a).

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