in archery should the arrow be aimed directly at the target? how should your angle of aim depend on the distance of the target? (AP physics)

dont arrows fall as gravity acts on them?

In archery, the angle of aim does depend on the distance of the target. The arrow should not be aimed directly at the target because it follows a curved path due to the force of gravity. To understand how to aim for different distances, we can consider the projectile motion equations from physics.

First, let's define some important terms:
- Range (R): The horizontal distance from the archer to the target.
- Initial velocity (v0): The speed at which the arrow leaves the bow.
- Launch angle (θ): The angle at which the arrow is shot from the horizontal.

Now, to find the optimal angle of aim for a specific range, you can use the following steps:

1. Determine the range (R) to the target.
2. Use the range formula for projectile motion: R = (v0^2 * sin(2θ)) / g. Here, "g" is the acceleration due to gravity (approximately 9.8 m/s^2).
3. Rearrange the formula to solve for the launch angle (θ): θ = (1/2) * arcsin((g * R) / v0^2).

By using this formula, you can calculate the launch angle needed to hit the target for a given range. Keep in mind that this formula assumes a flat, horizontal ground and neglects factors such as air resistance, wind, and the arrow's initial height.

In summary, when aiming in archery, you need to aim slightly above the target for longer distances to compensate for the effects of gravity and ensure the arrow reaches the desired distance.