Final answer:
The optimal sling angle to maximize the range of a projectile is 45 degrees. Other specific angle-related questions in physics have different optimal angles, for example, the maximum perpendicular weight component of a box on an incline is at 90 degrees, and simple harmonic motion for a pendulum is most accurate up to a 15-degree angle.
Step-by-step explanation:
The preferred sling angle for maximizing the range of a projectile launched from level ground is 45 degrees. This is because when air resistance is negligible, the optimal angle for a projectile to achieve maximum horizontal distance is 45 degrees. At this angle, the horizontal and vertical components of the initial launch velocity are equal, resulting in the longest possible range.
For a box on an inclined plane, the perpendicular component of the box's weight reaches its maximum at a 90 degrees incline, effectively when the plane becomes vertical and all of the box's weight acts perpendicular to the plane. As for pendulum motion, simple harmonic motion is a good model up to about 15 degrees of oscillation. Lastly, the angle formed between tangential velocity and centripetal force in circular motion is 90 degrees, as these two vectors are perpendicular to each other.