Final answer:
The acceleration due to gravity at an altitude where it is 50.0% of its value at the Earth's surface would require a much higher altitude than the options provided. The gravitational pull at altitudes such as 8,000 meters or 18,000 meters is less affected, so none of the given options are correct.
Step-by-step explanation:
The question at hand involves understanding how the acceleration due to gravity decreases with altitude above the Earth's surface. According to physics, the acceleration due to gravity is inversely proportional to the square of the distance from the center of the Earth.
At the Earth's surface, gravity's acceleration (g) is approximately 9.80 m/s². To find at what altitude the acceleration would be 50.0% of this, we use the formula for gravitational acceleration, g' = G * M / (r + h)², where G is the gravitational constant, M is the mass of the Earth, r is the radius of the Earth, and h is the altitude above the Earth's surface.
Setting g' to 50.0% of g and solving for h after inputting the known constants, we find that the altitude at which gravity is 50.0% of its surface value is not merely a few kilometers, but much higher. In reality, at altitudes of 8,000 meters or even 18,000 meters above the Earth's surface, the decrease in gravity is far less than 50%, meaning that all the options provided (A, B, C, D) are incorrect.
The correct option answer is: None of the above.