Question

The weight of an object above the surface of the Earth varies inversely with the square of the distance

from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from Earth's center,
what would it weigh if it were 4,010 miles from Earth's center?
Round your answer to two decimal places.

The body would weigh ______
pounds if it were 4,010 miles from Earth's center.

Answer 1

the body would weigh approximately 51.19 pounds if it were 4,010 miles from Earth's center.

Explanation:

To find the weight of the body when it's 4,010 miles from Earth's center, you can use the inverse square law for gravity, which states that weight varies inversely with the square of the distance. You can set up a proportion to solve for the weight:

Weight1 / Distance1^2 = Weight2 / Distance2^2

Where:

Weight1 = 50 pounds

Distance1 = 3,960 miles

Distance2 = 4,010 miles (what we want to find)

Weight2 = ?

Now, plug in the values and solve for Weight2:

50 / (3,960^2) = Weight2 / (4,010^2)

50 / (15,681,600) = Weight2 / (16,080,100)

To find Weight2, cross-multiply:

Weight2 = (50 * 16,080,100) / 15,681,600

Weight2 ≈ 51.19 pounds (rounded to two decimal places)