Question

A tracking station on Earth observes a rocket move away at 0.370c. This rocket is designed to launch a projectile at 0.505c relative to the rocket. What speed (in terms of the speed of light) does the tracking station measure for the projectile if it is fired (a) straight ahead of the rocket or (b) backward from the rocket?

Answer 1

given,

speed of rocket moving away = 0.370 c

speed of projectile = 0.505 c

a) Speed of the tracking station

u = 0.505 c + 0.370 c = 0.875 c

`u'= (u-v)/(1-(uv)/(c^2))`

`u'= ((0.875 c)-0.370 c)/(1-0.875 * 0.370)`

u' = 0.747 c

b) when the rocket is moving backward

u = -0.505 c + 0.37 c = - 0.135 c

`u'= (-v)/(1-(uv)/(c^2))`

`u'= ((-0.135 c-0.370 c)/(1-(-0.135) * 0.370)`

u' = -0.481 c

negative sign represent direction