Final answer:
Both the horizontally shot and dropped cannonballs hit the ground simultaneously because gravity accelerates them at the same rate, irrespective of their horizontal motion.
Step-by-step explanation:
The question is concerned with the projectile motion of two cannonballs: one that is shot horizontally and one that is dropped from the same height. According to the principles of physics, specifically projectile motion, horizontal and vertical motions are independent of each other. This means that the horizontal motion of the shot cannonball does not affect the rate at which it falls to the ground compared to the dropped cannonball.
Thus, assuming there is no air resistance, both cannonballs will hit the ground at the same time. This conclusion is based on the fact that gravity acts on both cannonballs equally, accelerating them towards the ground at the same rate, regardless of their horizontal velocities. In the case given, whether the cannonball is shot horizontally at 40 m/s or simply dropped, both will experience the same gravitational acceleration and hence, the time it takes for them to hit the ground will be the same.