Final answer:
To calculate the height above Earth where free-fall acceleration is 35% of its surface value, use the formula for gravitational acceleration at a distance from Earth and solve for the height h.
Step-by-step explanation:
The question asks at what height above the Earth the free-fall acceleration is 35% of its value at the Earth's surface. To find this height, we have to use the formula for gravitational acceleration g away from the Earth's surface, which is g' = G*M/(R+h)², where G is the gravitational constant, M is the Earth's mass, R is the Earth's radius, and h is the height above the Earth's surface. We know that g' = 0.35g, with g being the acceleration due to gravity at the surface. By setting up the equation 0.35g = G*M/(R+h)², we can solve for h.
We are given that Rearth = 6.37×10¶ m and g = 9.8 m/s². After substituting these values into the equation and simplifying, we end up with a quadratic equation in terms of h. Solving the quadratic equation will give us the value of h where the gravitational acceleration is 35% of g.