Final answer:
The range of a projectile is zero at angles of 90° or 0°. The optimum angle for maximum distance of a projectile is 45°, and the angle between tangential velocity and centripetal force vectors is always 90°.
Step-by-step explanation:
The question seeks to identify the angle at which the range of a projectile is zero and the optimum angle for maximum projectile distance. For a projectile, the range will be zero when it is launched vertically upward or not moving horizontally at all. This occurs at angles of 90° or 0° respectively. Furthermore, the optimum angle for a projectile to achieve maximum horizontal distance is 45°, taking into consideration that air resistance is negligible.
About the angle formed between the vectors of tangential velocity and centripetal force, it is a 90° angle since these vectors are perpendicular to each other.