Speed of light spacecraft

• Andrew Buren
This is because the speed of light is a fundamental physical barrier: it is the maximum speed an object can travel in a vacuum. So even if you had a rocket that could travel at half the speed of light, the bullet would still reach the speed of light before it ever hit the ground.So this is like the idea that objects within a black hole can appear to be exceeding c, even though they aren't?Yes, in a sense. Objects within a black hole can appear to be moving faster than they actually are, because they are moving relative to an outside observer.

Andrew Buren

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.)

If not, why?

Andrew Buren said:
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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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!

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

NWH said:
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.

HallsofIvy said:
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