Falling Monkey

Should a hunter aim his arrow above or below a falling monkey?


As usual, let's picture the scenario. A hunter slowly creeps up on a monkey hanging on a tree branch. He pulls out an arrow and steadies it while aiming at the monkey on the tree. The hunter knows that this monkey is very sensitive to noise. As soon as the arrow is released, the monkey will hear it and let go from the branch at that very instant. This means that as the arrow travels from the hunter on the ground to the monkey, the monkey will continue to fall. Now, the hunter has three options on how he wants to release his shot. Refer to the image in Figure 1. The first option is to shoot the arrow above the starting point of the monkey. The second option is to shoot the arrow directly at the starting point of the monkey. Finally, the third option is to shoot the arrow below the present spot of the monkey. Remember, the hunter wants to hit the monkey, while keeping in mind that the monkey will fall as his arrow travels.

Figure 1

Figure 2

Before we move on, let's talk about gravitational acceleration. Gravitational acceleration exists everywhere on the surface of earth. Mathematically, it is perceived as 9.8 meters/sec/sec. This means that every second, the speed of an object going down will increase by 9.8 meters per second. So, once the monkey drops it is at 0 m/s. After 1 second it reaches 9.8 m/s and after 2 seconds it should hit 19.6 m/s. Notice that gravitational acceleration is universal for all objects. That's right. Heavier objects do not fall faster than lighter objects. This is a very common misconception. People often believe this because the resistance from the wind can end up perturbating the speed of objects. The video in Figure 2 will prove this.

So we've come to the understanding that the monkey will fall with gravitational acceleration. What does this mean for our answer? The most important part to consider is that the arrow too, will fall with the same gravitational acceleration. This means the arrow till travel with a constant speed horizontally towards the monkey. While this happens, both the arrow and the monkey will fall the exact same vertical distance. As a result, the hunter would choose path 2. He would aim the arrow directly at the resting spot of the monkey, without worrying about it falling after. He doesn't need to worry about this becuase the arrow will fall the same amount. This is shown in Figure 3.

Figure 3