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Expert-verified Found in: Page 1147 ### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718 # Galaxy A is reported to be receding from us with a speed of 0.35c. Galaxy B, located in precisely the opposite direction, is also found to be receding from us at this same speed. What multiple of c gives the recessional speed an observer on Galaxy A would find for (a) our galaxy and (b) Galaxy B?

1. The multiple of c is 0.35.
2. The multiple of c is 0.62.
See the step by step solution

## Step 1: Describe the expression for the relativistic velocity of the particle

The relativistic velocity of the particle is given by,

Here, u is the velocity of the particle as measured in S, u' is the velocity of the particle as measured in S', v is the velocity of the S' relative to S, and c is the velocity of the light.

## Step 2: Determine the multiple of c for our galaxy(a)

If a person P is moving with speed v eastward from the person Q, then person P should observe that the person Q moving v away from person P.

In the similar way, if the Galaxy A is moving from our Galaxy with a speed of 0.35c then the observer in Galaxy A must see our Galaxy with the same speed of 0.35c or 0.35 multiple of c away from him.

Therefore the speed of an observer on Galaxy A from our galaxy is 0.35 multiples of c.

## Step 3: Determine the multiple of c for our galaxy B(b)

Rearrange the equation (1) as follows.

Substitute -0.35c for u and 0.35c for v in equation (2).

Here, the negative sign indicates the direction of the galaxy B with respect to the observer in galaxy A.

Therefore, the multiple of c is 0.62. ### Want to see more solutions like these? 