Final answer:
Initial velocity is the variable with the greatest effect on the minimum distance required for a projectile or vehicle to land or takeoff since the range is directly proportional to the square of its initial speed.
Step-by-step explanation:
The variable that has the single greatest effect on the minimum distance required to land or take off is the initial velocity of the projectile or vehicle in question. This is due to the fact that the range of a projectile is directly proportional to the square of its initial speed. When we apply this principle to aircraft and other vehicles, we understand that to achieve a shorter takeoff and landing, the vehicle must be capable of reaching a higher initial speed more rapidly.
For a projectile, the maximum range is achieved at an initial launch angle of 45°, however, this becomes approximately 38° when air resistance is taken into account. It's also important to understand that the value of the acceleration due to gravity is a factor. This was famously demonstrated by astronaut Alan Shepherd, who hit a golf ball on the Moon, where the weaker gravity allowed it to travel much farther than it would have on Earth.