Say you dropped a cannonball from the 17-meter mast of a ship sailing at 2 meters/second. How far from the base of the mast will the ball land?

It should land at the base of the mast. the cannonball, whilst in your hand, is travelling at the same rate as the boat in the horizontal plane ie at 2m/s. as it leaves you hand it should retain that velocity and therefore land right underneath where it was dropped. this assumes all other things are equal, eg there is no air resistance etc that might cause the ball to accelerate or decelerate.