Final answer:
In a vacuum, an arrow would impact with its tail first due to the absence of torque-inducing forces. However, with air resistance, the arrow will orient and impact headfirst because of the drag stabilization, where the feathers create more air resistance than the tip.
Step-by-step explanation:
To address whether an arrow would impact the ground with its tail when shot upwards in a vacuum (without air resistance), we can refer to projectile motion principles. In a vacuum, an arrow would indeed maintain its initial orientation throughout its flight because there are no external torques acting on it since gravity acts on all parts of the arrow equally.
This scenario is analogous to the idealized situations where a bullet is fired horizontally from a mountain, with gravity being the only force acting after it leaves the muzzle, as described in the provided references.
However, when air resistance is present, it does not treat all parts of the arrow equally. The feathers (fletching) at the end of the arrow create more air resistance than the tip, which causes the arrow to rotate and align with the direction of flight. This drag stabilization results from the air pushing more on the back end than on the tip, causing the arrow to rotate and eventually fall headfirst to the ground. The center of pressure being behind the center of mass is critical for this stabilization effect.
In summary, without air resistance, an object like an arrow follows a ballistic trajectory without self-orienting due to the absence of a torque-inducing force. However, with air resistance, the arrow orients itself due to the unequal distribution of air resistance across its length.