Final answer:
The range of a projectile is reduced by air resistance with an optimal angle of less than 45° when considering air resistance. The initial velocity significantly affects the range, and gravity influences it as well, as demonstrated by the increased range on the Moon due to weaker gravity.
Step-by-step explanation:
The question pertains to the range of a projectile with and without the influence of air resistance. When air resistance is ignored, the maximum range of a projectile occurs at an initial launch angle of 45°, and any two launch angles that sum to 90° yield the same range. With the presence of air resistance, however, the range is reduced, and the optimal angle for the maximum range is less than 45°, approximately 38°. The exact percentage of the range lost due to air resistance is dependent on various factors such as the shape, size, and speed of the projectile, and therefore cannot be precisely determined without additional information.
Furthermore, the initial velocity (ν₀) has a considerable impact on the projectile's range. The greater the initial velocity, the greater the range that can be achieved. This is also influenced by the value of the acceleration of gravity (g), which affects the range, as lighter gravity on the Moon allows for a farther range than on Earth.