Final answer:
A person who can jump a distance of 3.0m on Earth could jump approximately 18.0m on the Moon, given that the Moon's gravitational acceleration is about 1/6th that of Earth's.
Step-by-step explanation:
When we consider how gravitational acceleration affects the jumping distance of an individual, it's important to understand the relationship between gravity and motion in a projectile (which is effectively what the person becomes when they jump). On Earth, the acceleration due to gravity is approximately 9.8 m/s², and on the Moon, it is about 1/6th of that value, or approximately 1.6 m/s².
If a person can jump a horizontal distance of 3.0 m on Earth, we know that the same person under lunar gravity, without any change in their takeoff speed or angle, should be able to jump six times as far, since the downward acceleration is six times less. Therefore, the horizontal jumping distance on the Moon would be 3.0m multiplied by 6, which equals 18.0 m.
So, even though the options given (0.5m, 1.0m, 1.5m, and 2.0m) don't include the correct answer, we can deduce that the increased distance is significantly more than 2.0m, considering the reduced gravitational pull on the Moon.