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Relative motion is a key concept to understand when dealing with projectile motion in scenarios like the one described with the zookeeper and the monkey. In physics, relative motion refers to the calculation of the movement of an object with regard to some other moving object.
This is particularly important because it allows us to analyze movements in non-inertial frames of reference, where multiple objects are in motion simultaneously.
When you fire the tranquilizer gun, the dart and the monkey exhibit relative motion, moving towards each other. However, both are also subject to uniform acceleration downward due to gravity.
In this scenario, it is essential to recognize that even though the monkey and the dart are moving in different directions, the relative vertical movement is synchronized because of gravity's constant effect on both objects.
Therefore, by aiming directly at the monkey initially, you account for their shared acceleration due to gravity, making their trajectories coincide throughout the fall.

Gravity is the invisible force that pulls objects towards one another, and it plays a central role in the exercise at hand. It affects all objects with mass, and on Earth, it gives weight to physical objects and causes them to fall to the ground when dropped.
The concept of gravity is fundamental when analyzing projectile motion because it consistently accelerates objects toward the center of the Earth at approximately 9.81 m/s².
In our scenario with the zookeeper and the monkey, both the tranquilizer dart and the monkey are subjected to this same gravitational acceleration.
This is critical to understand because it implies that, once in motion, their vertical motion components are identical due to gravity alone. This shared acceleration ensures that regardless of their initial horizontal positions, they will continue to descend at the same rate, ensuring the dart will meet the monkey mid-descent.

To thoroughly understand projectile motion, it is necessary to break down the motion into horizontal and vertical components. This separation allows us to analyze the movement in each direction separately, which is useful in understanding the overall path.
The horizontal component of a projectile's motion, such as that of the tranquilizer dart, remains constant if we neglect air resistance—the speed doesn't change because there is no horizontal acceleration.
Meanwhile, the vertical component is where gravity comes into play, constantly accelerating the object downward.
In the zookeeper's task, aiming directly at the monkey accounts for both components of motion.

• The horizontal component ensures the dart remains on a straight path toward the initial position of the monkey.
• The vertical component, checked by gravity, ensures that both the dart and monkey fall without any influence from horizontal motion.

By merging these components, the dart and monkey follow similar paths, leading to a successful tranquilizing shot at the monkey's moving position.