1. The problem statement, all variables and given/known data Imagine that you are an observer in space (so you are in an inertial system), when the cannon (located on the equator) fires a cannonball in north direction. What does the trajectory of the cannonball look like from your perspective? Is it a straight line (that would mean that the cannonball is not affected by Earth's rotation) or something like a spiral? 2. Relevant equations 3. The attempt at a solution I think that, since the only real force acting on the body is the gravitational force, the trajectory is like a spiral. I also know that no Coriolis force exists in my inertial frame of reference. Am I right?
The question is not so clear for me. This is what I think- If you consider the earth to be an inertial frame of reference, then the trajectory of the ball would be a straight line. If you consider the earth to be a non-inertial frame of reference (take its rotation in account), then the trajectory of the ball would be similar to a spiral. In both the above cases, you are in an inertial frame of reference, so there will not be any Coriolis force.
If you don't shoot the cannonball faster than escape velocity, the orbit will be an ellipse. Look up two-body problem. Of course the ellipse will intersect the surface of the earth again at some point.