Question

In archery, should the arrow be aimed directly at the target? How should your angle of aim depend on the distance to the target?

Short answer

The arrow should be aimed a bit higher than the target. The angle of the aim depends upon the distance from the target.

Step-by-step solution

Step 1. Understanding projectile motion

When an object is launched under the influence of gravity, it is said to be undergoing projectile motion. The path followed by the object undergoing projectile motion is parabolic.

Step 2. Archery and projectile motion path

When an arrow is fired, the only force acting on it is gravitational pull. The following figure shows that the object is undergoing projectile motion. It follows a curved parabolic path instead of a straight-line path. Thus, the arrow also follows a parabolic path.

Step 3. Understanding the angle at which the arrow should be aimed to hit the target

An object launched under the influence of gravity follows a parabolic path and not a straight-line path. So, the arrow cannot be aimed directly at the target. It needs to be aimed a bit higher than the bull’s eye to counter the effect of gravity.

As the distance from the target increases, the angle needs to be adjusted accordingly. So, the projectile still covers the required horizontal distance. The angle depends on the horizontal distance and the gravitational effect of the space.