# Speed of light spacecraft

## Main Question or Discussion Point

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.)

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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

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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.

NWH
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
Homework Helper
So this is like the idea that objects within a black hole can appear to be exceeding c, even though they aren't?
Since we cannot observe an object within a black hole, I have no idea what "appear" can mean here.

NWH
Since we cannot observe an object within a black hole, I have no idea what "appear" can mean here.
Hypothetically speaking, of course...

ccording to Einstein's special theory of relativity, objects gain mass as they accelerate to greater and greater speeds. Now, to get an object to move faster, you need to give it some sort of push. An object that has more mass needs a bigger push than an object with less mass. If an object reached the speed of light, it would have an infinite amount of mass and need an infinite amount of push, or acceleration, to keep it moving. No rocket engine, no matter how powerful, could do tthis