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Chapter 6: Q3E (page 1247)

How fast must a rocket travel relative to the earth so that time in the rocket 鈥渟lows down鈥� to half its rate as measured by earth-based observers? Do present-day jet planes approach such speeds?

Short Answer

Expert verified

u = 0.867c

Step by step solution

01

Concept of the time dilation equation

The time dilation equation is given as鈭�t=纬鈭�t0/1-u2/c2where鈭�t0 is the proper time in the rest frame,鈭�tis the time interval measured in the second frame of reference u is the speed of the second frame with respect to the rest frame, c is the speed of light

02

Calculate the speed of the jet plane.

We know that,螖t=12螖t0 In order to calculate the u of the rocket, we will use the time dilation equation: 螖t=纬螖t0

y=1-u2/c2鈭�t=鈭�t0/1-u2/c21-u2/c2=鈭�t0/鈭�t

By squaring both sides:

1-u2/c2=122u2/c2=1-122

By taking square root for both sides:

u2/c2=1-122uc=0.867u=0.867c

The fastest jet plane is around1.09脳103m/s

Thus, there is no jet plane nowadays approaches such speeds.

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