Question

Galaxy B moves away from galaxy A at 0.577 times the speed of light. Galaxy C moves away from galaxy B in the same direction at 0.731 times the speed of light. How fast does galaxy C recede from galaxy A?

Answer 1

Answer:

The value is  $p = 0.7556 c$

Explanation:

From the question we are told that

   The speed at which galaxy B moves away from galaxy A is  $v = 0.577c$

Here c is the speed of light with value  $c = 3.0 *10^{8} \ m/s$

     The speed at which galaxy C moves away from galaxy B is  $u = 0.731 c$

Generally from the equation of  relative speed we have that  

     $u = \frac{p - v}{ 1 - \frac{ p * v}{c^2} }$

Here p is the velocity at which galaxy C recede from galaxy A so

     $0.731c = \frac{p - 0.577c }{ 1 - \frac{ p * 0.577c}{c^2} }$

=>   $0.731c [1 - \frac{ p * 0.577}{c}] = p - 0.577c$

=>   $0.731c - 0.4218 p = p - 0.577c$

=>   $0.731c + 0.577c = p + 0.4218 p$

=>   $1.308 c = 1.731 p$

=>    $p = 0.7556 c$