Final answer:
By comparing the acceleration due to gravity on a different planet to Earth's, we can calculate that if a boy can safely jump from 2 meters on Earth, he could safely jump from a height of 10 meters on the planet where gravity is 1.96 m/s². Therefore, the correct option is D.
Step-by-step explanation:
To determine the safe height from which a boy could jump on another planet, we need to consider the acceleration due to gravity on that planet compared to Earth. The acceleration due to gravity on Earth is approximately 9.80 m/s². On the planet in question, the acceleration due to gravity is 1.96 m/s², which is about ⅖ or 0.2 times that of Earth's gravity.
If the boy can safely jump from 2 meters on Earth, then to find the corresponding safe jumping height on the other planet, we can set up a ratio. The safe height on the other planet would be inversely proportional to the relative accelerations due to gravity. This means that if gravity on the other planet is 0.2 times as strong, the safe height would be 5 times greater (1 divided by 0.2).
Therefore, the safe height on the planet would be 2 m multiplied by 5, which equals 10 meters. The correct answer is D. 10 m.