Part A Have you aged more or less than your friends at home? Submit My Answers G

Question

Part A

Have you aged more or less than your friends at home?

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Correct

Here we learn how to apply the expression for time dilation to determine that a moving person aged less.

Part B

By how much?
Hint: Use the binomial approximation.

Express your answer with the appropriate units.

3.47ns

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You fly 5000 km across the United States on an airliner at 200 m/s . You return two days later traveling at the same speed. You may want to review ( pages 1035 - 1039) .

Part A

Have you aged more or less than your friends at home?

SubmitMy AnswersGive Up

Correct

Here we learn how to apply the expression for time dilation to determine that a moving person aged less.

Part B

By how much?
Hint: Use the binomial approximation.

Express your answer with the appropriate units.

3.47ns

SubmitMy AnswersGive Up

Incorrect; Try Again; 6 attempts remaining

Explanation / Answer

Immediately we can see that the time dilation will be negligible: v/c = (2*10^2)/(3*10^8) = 0.67*10c m/s.

But working ahead anyway, we must use three inertial reference frames (if we ignore the acceleration experienced during take-off and landing).

1) The people staying at home.

2) Your flight away from home

3) Your return flight

The time it takes as measured by your friends at home to go 5000 km at 200 m/s is 5000000/200 = 25,000 sec. Using the time dilation formula t'=t, where t is the proper time, =1/sqrt(1-(v/c)²), and t' is the time measured by your friends. Solving for t: t = t'/

In this case =1.0000000000005, and thus, you measure the amount of time elapsed as 25000/1.0000000000005 = 24999.99999999 sec. We can solve the third inertial reference frame (return trip) in a similar manner, and we find that your friends at home measure 20000 sec again, while you measure 24999.99999999 sec.

In total, you age approx 2*10^-8 sec less than your friends at home.

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