Question

At what height above the earth is the free-fall acceleration 30 % of its value at the surface? assume rearth = 6.37 × 10 6 m .

Answer 1

The height above the Earth where the free-fall acceleration is 30% of its value at the surface is approximately 5.30 × 10^6 m.

Step-by-step explanation:

To determine the height above the Earth where the free-fall acceleration is 30% of its value at the surface, we can use the formula for gravitational acceleration:

g' = g * (1 - (2 * r) / (3 * h))

Where:

• g' is the free-fall acceleration at a height above the Earth
• g is the acceleration due to gravity at the surface of the Earth
• r is the radius of the Earth
• h is the height above the Earth

Given that g' = 0.3g and r = 6.37 × 10^6 m, we can solve for h using the formula above. After substituting the values and solving, we find that the height above the Earth is approximately 5.30 × 10^6 m.