Final answer:
The zookeeper should aim the banana cannon directly at the monkey, since gravity will cause both the banana and the monkey to fall the same distance at the same time, ensuring that the banana hits the monkey.
Step-by-step explanation:
The question is a classic physics problem that involves projectile motion and the independence of horizontal and vertical motions. If the zookeeper shoots the banana from the banana cannon, they should aim directly at the monkey. Assuming there is no air resistance, gravity acts equally on both the banana and the monkey the moment the banana is fired and the monkey lets go. Therefore, regardless of the initial velocity of the banana, as long as the banana is aimed at the monkey, they both will fall the same vertical distance over the same amount of time. Consequently, the banana will reach the monkey's position as they both descends downward.
This principle of projectile motion is often tested in high school physics courses, and it illustrates an important property of gravity: its effect on falling objects is independent of the object's initial horizontal motion. The famous thought experiment with the monkey and the hunter, where the monkey drops when the hunter fires the bullet and still gets hit, is analogous to this scenario with the banana and cannon.
Understanding this concept helps in solving other projectile motion problems, such as firing a watermelon from a slingshot or aiming a water balloon cannon to hit a target at a certain distance. It is an essential concept in mechanics that highlights the predictable nature of projectile trajectories under the influence of gravity.