Final answer:
Given that the moon's gravity is 1/6th of Earth's, the horizontal distance a person could jump on the moon would be √6 times further than on Earth. For a horizontal jump of 2.07 m on Earth, this would be approximately 5.07 m on the moon.
Step-by-step explanation:
To determine how far a person could jump on the moon compared to on Earth, we need to understand that the horizontal distance covered in a jump (assuming the same initial velocity) is related to the time of flight. The time of flight, in turn, is affected by the acceleration due to gravity. On the moon, the acceleration due to gravity is 0.202g, where g on Earth is approximately 9.80 m/s². Therefore, on the moon, the acceleration due to gravity would be 0.202 × 9.80 m/s², which is approximately 1.98 m/s². The time of flight of a projectile (or a jumping person in this case) is directly proportional to the gravitational acceleration. Since the moon's gravity is 1/6th of Earth's, the time of flight on the moon would be √6 times longer, because the time of flight depends on the square root of 1/acceleration due to gravity. This implies that the person would be able to jump √6 times further on the moon compared to their 2.07 m jump on Earth. So, the horizontal distance that could be jumped on the moon is √6 × 2.07 m which equals approximately 5.07 m.