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Chapter 36: Q. 19 (page 1059)

You fly 5000kmacross the United States on an airliner at 250m/s.You return two days later at the same speed.

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

b. By how much?

Hint: Use the binomial approximation

Short Answer

Expert verified

a.)Because my proper time is smaller than the time in the Earth frame, I have aged less.

b.)In frame S鈫�鈭�t=4脳104s,

In frame S'鈫�鈭�蟿=14ns

Step by step solution

01

Part (a) Step 1: Given Information

We have given that,

Airliner takes of and attains v=250m/s.

Airliner returns to original position after 2days.

We have to assume you've aged more or less than your family and friends.

02

Part (a) Step 2: Simplify

Because my proper time is smaller than the time in the Earth frame, I have aged less.

03

Part (b) Step 1: Given Information

We have given that,

Airliner takes of and attains v=250m/s.

Airliner returns to original position after 2days.

We need to figure out how much is the Earth's frame and the airliner's frame.

04

Part (b) Step 2: Simplify

The Earth's frame is S.

The Airliner's frame is S'.

In the Sframe:

鈭�t=2脳5脳106m250m/s鈭�t=4脳104s

In the frameS':

鈭�蟿=鈭�t1-v2c21/2鈭�蟿=鈭�t1-v22c2鈭�蟿=鈭�t路v22c2鈭�蟿=(4脳104s)12250m/s3脳108m鈭�蟿=1.4脳10-8s鈭�蟿=14ns

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