Question

Two spacecrafts are getting closer from each other with the same speed as measured by an observer on Earth. If the relative speed of the two spacecrafts is 0.7c, find the speed of each spacecraft as measured on Earth.

Answer 1

from the addition of velocities

v = ux - (-v)/ 1- ux (-v)/ c^2

= ux + v/ 1 + ux v / c^2

0.7 c ( 1 + ux v / c^2) = ux + v

since both space ships have same speed uc = v

0.7 c( 1+ v^2/c^2 ) = 2v

0.7* v² - 2 * v *c + 0.7 *c²

solving quadratic equation

v= 7.35 * 10^8 or 1.23* 10^8 m/s

the first option is wrong because no object can attain velocity greaterthan that of light,

v= 1.23 * 10^8 m/s ( c/3* 10^8 m/s) = 0.41 c

so the space ships are moving with velocities 0.41 c