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Chapter 37: 30P (page 1147)

Stellar system Q1 moves away from us at a speed of 0.800c. Stellar system Q2, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q2 as measured by an observer in the reference frame of Q1?

Short Answer

Expert verified

The multiple of c is 0.588.

Step by step solution

01

Describe the expression for the velocity of the particle

The relativistic velocity of the particle is given by,

u=u'+v1+u'vc 鈥︹�� (1)

Here, data-custom-editor="chemistry" u=0.400c is the velocity of stellar Q2 in reference frame, and data-custom-editor="chemistry" u=0.800c is the velocity of the reference frame of the observer on stellar Q1 relative to the reference frame.

02

Determine the multiple of c

Rearrange the equation (1) for u'.

u1+u'vc2=u'+vuu'vc-u'=v-uu'uvc2-1=v-uu'=v-uuvc2-1 鈥︹�� (2)

Substitute 0.800c for v, and 0.400c for u in equation (2).

u'=0.800c-0.400c0.800c0.400cc2-1=0.400c0.32-1=-0.588c

Here, the negative sign indicates the opposite direction.

Therefore, the multiple of c is 0.588.

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