Is gravity significant in this scenario?

[Cheddar]

Homework Statement

A large gun accelerates a 5.0 kg mass from rest to a speed of 4000 m/s into orbit. The net force accelerating the bullet is 490,000 N.
How long will it take the projectile to come up to speed?
It doesn't say anything above air resistance or gravity.

Homework Equations

acceleration = net force / mass
time = velocity / acceleration

The Attempt at a Solution

0.041 seconds (using the equations listed above)
What about gravity? Was this already calculated into the net force?

 

[tiny-tim]

A large gun accelerates a 5.0 kg mass from rest to a speed of 4000 m/s into orbit.

Hi Cheddar!

This question doesn't make any sense …

if the mass goes into orbit, the orbit obviously passes through the end of the gun …

in other words, if the gun is on Earth, then the mass crashes, and doesn't go into orbit.

 

[Kaimyn]

I think I might have heard something along these lines. Does it have anything to do with this?

Good ol' Newton

Perhaps when it says large, it really means large

 

[Redbelly98]

The Attempt at a Solution

0.041 seconds (using the equations listed above)

Looks good, I think the problem is just this simple ... though tiny-tim is correct, since the gun is presumably on the surface of the Earth it will return to Earth after one single orbit (neglecting air resistance).

What about gravity? Was this already calculated into the net force?

A reasonable question. Try comparing the force of gravity to the 490,000 N force being applied.

 

[tiny-tim]

I think I might have heard something along these lines. Does it have anything to do with this? …

ah! thanks Kaimyn! … the ol' do-it-from-the-top-of-Mount-Everest trick!

in that case, Cheddar, you can forget about gravity …

the gun, and the acceleration, will be horizontal (and the mass will be supported by the bottom of the barrel of the gun ).

 

[Redbelly98]

Perhaps when it says large, it really means large

The acceleration occurs over roughly 80 meters, very small compared to the size of the Earth.

But the orbit issue really is irrelevant here.

 

[The_Doctor]

4000/(490000/5) What they're basically asking is how long will it take to reach 4000m/s.

 

[Cheddar]

Thank you everyone for your input.
Now, I realize that the fact that the mass is being projected into orbit doesn't matter.
Since the speed of the mass is going to reach 4000 m/s well before reaching orbit.
The question is whether my answer correct as it is (neglecting gravity) or should I be accounting for gravity at some point in the equations?

 

[Redbelly98]

The question is whether my answer correct as it is (neglecting gravity) or should I be accounting for gravity at some point in the equations?

I repeat:

Try comparing the force of gravity to the 490,000 N force being applied.