If cannon at 45 north latitude is fired due north, will the cannon ball land east or west from the meredian?

Question

Ignore air resistance.

Bekki,
I tried to point my finger at direction of
the motion but,

But it looks like the direction of the motion is changing.... and changing....

Normal cannon, small range. Well, maybe howitzer....

Answer 1

East. Obvious way to tell: the coriolis force drives stuff clockwise in the northern hemisphere.

If you want something mathier:

Coriolis acceleration: - (omega)x(velocity)

So put your right fingers in the direction of the rotation (in the direction the north star). Put your palm in the direction of the motion. Your thumb points west. But the answer is east because of the minus sign.

Edit--in the case of a storm, the direction changes and the coriolis force pushes it around in a circle. In the case of your cannon ball, it's probably safe to assume that the coriolis force is just a minor perturbation to the flight. It still goes north pretty much, but the coriolis force pushes it a wee tiny bit east of north. And remember, of course, that when you use the pseudoforces (coriolis, centripetal, etc), you've already taken rotation into account, so you don't have to worry about the earth spinning.

Answer 2

East. Let's imagine that the local area of the cannon range is non-spherically flat and moving with some speed east. Since motion is relative, a cannon shot fired north will land due north even as this local range is moving eastward. However, the north-south axis of the spherical local area is actually rotating counterclockwise due to the Earth's rotation. so by the time the cannon shot lands, it will have landed to the east of the meridian. This assumes that the cannon range is relatively small compared to the size of the globe, as the problem becomes more complicated once orbitals are involved.

Addendum: This answer assumes that the cannon itself was travelling with the surface of the Earth. Obviously, if the instantaneous velocity vector of the cannon shot was exactly north, then it'd land "west" of the meridian.

Answer 3

Assuming the cannon is small relative to the globe.
Assuming the cannon is attached to the globe.
The cannon and the ball (and the underlying ground) is traveling East due to the rotation of the Earth before it is fired.
There, the cannon ball has an Eastward component of the velocity when fired North. As the ball approaches the North pole the velocity of the Earth traveling East is less. (Because the diameter of the latitude is less, than at lower latitudes.)
Therefore the cannon ball is traveling East faster than the underlying ground.

Answer 4

East