RQ wrote:I suppose you're right, but my thought was that suppose let's say that the ship was traveling at say half the speed of light, and it sent out a rocket that traveled at 3/4 the speed of light, the rocket would then travel faster than light by one quarter.
You are assuming that it is possible to simply add the speeds (that is, 1/2 + 3/4 = 5/4). This is correct in "Newtonian" physics, but in fact, the formula is NOT true for relativity.
Instead, if there is a rocket traveling with speed u (relative to you), which then fires a rocket in the same direction with speed v, the speed of the rocket (relative to you) is:
(u+v)/(1+(uv/c^2))
This formula can be found in both my Physics textbook and at many websites (ex.
http://hyperphysics.phy-astr.gsu.edu/hb ... invel.html)
Thus, for the original problem, the velocity of the rocket relative to you is:
(0.5c + 0.75c)/(1+(0.5*0.75))
(1.25c)/(1.375)
(10/11)c
This is closer to the speed of light than either 0.5c or 0.75c, but its still less than the speed of light.