# Speed of light spacecraft

If you had a spaceship travleing at half the speed of light then shot a bulit at half the speed of light again, would the bulit appear to go the speed of light relative to an outside obverver?
(All preposed in theory, of cource.)

Related Special and General Relativity News on Phys.org
If not, why?

Doc Al
Mentor
If you had a spaceship travleing at half the speed of light then shot a bulit at half the speed of light again, would the bulit appear to go the speed of light relative to an outside obverver?
(All preposed in theory, of cource.)
No. To find the speed of the bullet with respect to that outside observer, you must use the relativistic addition of velocity formula:

$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

Which gives: (0.5c + 0.5c)/(1 + (.5)^2) = 0.8 c

Last edited:
HallsofIvy
Homework Helper
The "outside observor" being assumed to be one relative to which the spaceship is moving at (1/2)c, of course. There can exist "outside observors" with other speeds relative to the spaceship!

Doc Al
Mentor
Good point.

So this is like the idea that objects within a black hole can appear to be exceeding c, even though they aren't?

Hi there,

But no matter what, the bullet would never have c for any observer, in any relative frame.

Cheers

HallsofIvy