Could a projectile shooting downward at near c lift 300lbs?

[falafel1995]

If a 1 pound projectile was shot out of a stationary, non-fixed object (downward) near the speed of light (on earth) would it lift the object if it were 300 pounds? If so, how far?
My friend and I were arguing a hypothetical similar to this.

 

[Curl]

Very far because the momentum of a projectile "near c" is exceedingly large.

 

[Antiphon]

How far would you like it lifted, sailor?

As you've stated it, and as Curl says, I could land the 300lb object on your favorite neutron star with enough force left over to turn it into a black hole.

 

[KingNothing]

Of course. The initial speed of the 300-pound object will be 1/300th the speed of the 1-pound object. There's nothing magical about a large size difference.

 

[Ryan_m_b]

If so, how far?

All the way! More seriously the escape velocity for Earth is ~11kmps, your 300 pound object would be traveling at a speed far greater than this so would shoot straight out of the atmosphere (friction with the atmosphere would cause serious damage but never mind that for now) and straight out of the solar system

 

[falafel1995]

How fast would this object go, assuming no friction?

 

[Ryan_m_b]

How fast would this object go, assuming no friction?
PS: I don't think 1/300 the speed of light is not fast enough to escape the solar system with respect to the milky way's gravity, ~525 km/s vs ~302 km/s.

Erm, 1/300th of the speed of light is 1,000km/s. Did you misquote your figures or the calculation?

 

[falafel1995]

Erm, 1/300th of the speed of light is 1,000km/s. Did you misquote your figures or the calculation?

I reworked it. It was calculations.

 

[russ_watters]

You guys didn't consider Relativity. The initial speed of the 300lb object would be much greater than 1/300th that of the 1lb object.

 

[JArkinstall]

How far would it go?

It will leave Earth's gravitational field with a fair amount of velocity - whether or not you're taking relativity into account. Of course that's assuming the object is small, I'm not sure how much drag one could get at very large sizes.

Anyway, once it's left the gravitational field, it will keep moving at an almost constant speed (Newton Law #1) - neglecting influences from other bodies. So, as long as it has a clear path, a very long way away indeed.