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Chapter 6: Q8E (page 1248)

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its search light blink on for 0.150 s. The first officer on the spacecraft measures that the searchlight is on for 12.0 ms. (a) Which of these two measured times is the proper time? (b) What is the speed of the spacecraft relative to the earth, expressed as a fraction of the speed of light c?

Short Answer

Expert verified

A)螖t0=0.012sb) u=0.997c

Step by step solution

01

Concept of the time dilation equation.

The time dilation equation is given as螖迟=纬螖迟0/1-u2/c2where 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 proper time and the speed of spacecraft

The searchlight which blinked on is the searchlight of the spacecraft, so the event happened in the first officer frame of reference. Thus, the proper time螖迟0=12ms=0.012s is the time that was measured by the first officer on the spacecraft.

1s=1000ms鈭�t0=121000=0.012s

Thus,螖迟0=0.012s

By the time dilation equation,

role="math" localid="1664086479811" 鈭�t=纬鈭�t0鈭�t0=11-u2c2鈭�t0.150=11-u2c2脳0.012=0.997c

Therefore, u=0.997c

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