Final answer:
The range of a projectile is influenced by its initial velocity and launch angle, reaching a maximum when the angle is 45 degrees in a vacuum. Air resistance and gravity also significantly affect projectile motion, altering the optimal conditions for achieving maximum range.
Step-by-step explanation:
The question pertains to the range of a projectile, which is the maximum horizontal distance traveled by the projectile when it is projected at an initial angle with respect to the horizontal axis. The initial velocity of a projectile is a critical factor affecting its range. The formula explaining this relationship, assuming no air resistance and that the projectile lands at the same elevation from which it was launched, is given by R = (v02 sin 2θ0) / g, where R is the range, v0 is the initial speed, θ0 is the launch angle, and g is the acceleration due to gravity. The maximum range is achieved when the launch angle is 45° in the absence of air resistance. If air resistance is considered, the optimal launch angle shifts to approximately 38°. Additionally, because gravity varies in strength in different celestial environments, like the Moon, the range can also be significantly affected by the local acceleration due to gravity.