Question 153914: The formula: R (sub a) = R (sub f)sqrt{1-(v/c)^2}
expresses the aging rate of an astronaut. R (sub a), relative to the aging rate of a friend on Earth, R (sub f), where v is the astronaut;s velocity and c is the speed of light.
a. Find lim_v-c R (sub a)
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.
I know it's long but thanks for everyone's help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The formula: R (sub a) = R (sub f)sqrt{1-(v/c)^2}
expresses the aging rate of an astronaut. R (sub a), relative to the aging rate of a friend on Earth, R (sub f), where v is the astronaut;s velocity and c is the speed of light.
a. Find the limit as v goes to c of R (sub a)
As v goes to c (v/c) goes to 1; sqrt(1-(v/c)^2) goes to zero; R(sub a) goes
to zero.
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?
I stay young and the earthling ages.
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c. Explain why a left-hand limit is used in part a.
The left-hand limit will be positive implying there is some aging.
A right-hand limit would be negative implying the space traveler
was getting younger.
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Cheers,
Stan H.
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