The Monkey and Zookeeper

Aiming at the Monkey - Fast

Suppose a zookeeper must shoot a banana from the banana cannon to a monkey who hangs from the limb of a tree. This particular monkey has a habit of dropping from the tree the moment that the banana leaves the muzzle of the cannon. The zookeeper is faced with the dilemma of where to aim the banana cannon in order to hit the monkey. If the monkey lets go of the tree the moment that the banana is fired, then where should she aim the banana cannon? To ponder this question, consider the scenario in which the zookeeper aims at the monkey and shoots the banana very fast (perhaps she presumes that if shot fast enough, the banana will hit the monkey before it falls very far). What would be the path of the banana? Would the banana hit the monkey?

As is obvious from the animation above, the banana moves in a parabolic path in the presence of gravity. In the presence of gravity, the monkey also accelerates downward once he lets go of the limb. Both banana and monkey experience the same acceleration since gravity causes all objects to accelerate at the same rate regardless of their mass. Since both banana and monkey experience the same acceleration each will fall equal amounts below their gravity-free path. Thus, the banana hits the monkey. Since the banana left the muzzle moving very fast, the banana reaches the monkey before the monkey has fallen very far. Now let's suppose that the zookeeper aims at the monkey but shoots the banana with a slow speed. Will this lead to success?

To further study the Monkey and Zookeeper dilemma and see additional animations, click on one of the following links.

The Monkey and The Zookeeper

Throw at the Monkey in a Gravity Free Environment

Throw above the Monkey with Gravity On

Throw at the Monkey at a Slow Speed with Gravity On
 

Click on any of the above links to explore the zookeeper's dilemma.

For more information on physical descriptions of motion, visit The Physics Classroom Tutorial. Detailed information is available there on the following topics:

Acceleration of Gravity

Acceleration of Gravity and the Independence of Mass

Projectiles

Characteristics of a Projectile's Trajectory