Final answer:
The angle at which the range of a projectile is zero is either 90° or 0°, as these angles mean a projectile goes straight up or has no vertical motion, respectively. The optimum angle for a projectile to achieve maximum range is 45°, which balances the vertical and horizontal velocity components.
Step-by-step explanation:
When analyzing the trajectory of a projectile, various angles result in different ranges and distances. The range of a projectile is the horizontal distance it travels before landing. If we launch a projectile at an angle of 90°, it will go straight up and fall back down to its starting point, meaning the horizontal range is equal to zero. This also applies if we launch a projectile at 0°, as it will not have a vertical component and thus, no actual projectile motion occurs. Therefore, the correct answer for the angle at which the range of a projectile is equal to zero is option c, 90° or 0°.
The optimum angle for a projectile to achieve maximum range on a flat surface, without any air resistance, is 45°. At this angle, the vertical and horizontal components of the velocity are equal, providing the ideal balance between the time the projectile spends in the air and the horizontal distance it covers. Thus, the answer for the optimum angle to launch a projectile is option b, 45°.