Vertical Missile Launch: Will it Hit Its Target After 20 Minutes?

[darkar]

Let say u can fire a missile vertically, and it will only return to ground after 20 mins, will the missile hit right on where it was fired?

P/s: Assuming there is no resistance.

 

[whozum]

If no wind resistance, yeah.

 

[Pengwuino]

Sure will. And it'll land completely vertically too

 

[PeteSF]

If you fire it from one of the Poles, yes. Otherwise, no.

Coriolis...

 

[whozum]

Pete, can you explain your position?

The coriolis effect diminishes when neglecting wind resistance, and also according to this site is zero at the equator, not the poles:

The amount of deflection the air makes is directly related to both the speed at which the air is moving and its latitude. Therefore, slowly blowing winds will be deflected only a small amount, while stronger winds will be deflected more. Likewise, winds blowing closer to the poles will be deflected more than winds at the same speed closer to the equator. The Coriolis force is zero right at the equator.

http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml

 

[Meir Achuz]

The angular momentum of the missile is conserved.
$$L=mr^2\omega$$.
As r increases, $$\omega$$ will become smaller.
The missile will land to the West of you., except at a pole, as Pete said.

 

[whozum]

Can you define your variables? mr^2 represents the moment of inertia which doesn't change during the course of flight, so I don't see why any of this should happen.

Also close your tex tags with a / not \

 

[DaveC426913]

If you neglect air resistance, this can be seen as an orbital mechanics problem.

The missile's initial trajectory is the sum of it upward boost, plus its eastward velocity imparted by the rotation of the Earth.

The moment its rocket shuts off, it is in orbit about the Earth's centre of mass. The orbit is elliptical.

When it reaches the Earth's surface on the return part of its orbit, 20 minutes later, the Earth will have rotated by 5 degrees.

 

[Meir Achuz]

My r was the distance from the center of the Earth, which increases as the rocket goes up.

 

[whozum]

If you neglect air resistance, this can be seen as an orbital mechanics problem.

The missile's initial trajectory is the sum of it upward boost, plus its eastward velocity imparted by the rotation of the Earth.

The moment its rocket shuts off, it is in orbit about the Earth's centre of mass. The orbit is elliptical.

When it reaches the Earth's surface on the return part of its orbit, 20 minutes later, the Earth will have rotated by 5 degrees.

Since v < v_esc, it doesn't breach the atmosphere and it remains with the earth, its rotating along with it, isn't it? The same reason a helicopter doesn't land west of where it started while hovering in the same place?

 

[DaveC426913]

Since v < v_esc, it doesn't breach the atmosphere and it remains with the earth, its rotating along with it, isn't it? The same reason a helicopter doesn't land west of where it started while hovering in the same place?

The initial post clearly indicates discounting air reisistance. This post ws a waste of time and space.

 

[whozum]

So your saying BECAUSE there's no air resistance the rocket will land to the west?

If the space is bothering you feel free to delete the post, but I'm sorry if I wasted 8 seconds of your life reading that ;)

 

[PeteSF]

Hi whozum,
Yes, that's right. In this case, air resistance (if the air is moving with Earth, ie no crosswind) helps to keep the rocket over the launch pad.

I'm a bit fuzzy on the details of Coriolis, but I think it works differently for North-South motion (zero at Equator, max at Poles) that for vertical motion (zero at poles, max at Equator).