the weight of a body above the surface of earth varies inversely with the square of the distance from the center of the earth. if maria weighs 125 pounds when she is on the surface of the earth(3960 miles from the center),determine maria weight if she is at the top of mount McKinley(3.8 miles above the surface of the earth)
Mt McK is
(3960+3.8)/3960 = 1.0009595... as far as the radius of earth.
So, the weight there = 125/(1.0009595)^2
thank u steve
To solve this problem, we need to use the concept of inverse variation and the inverse square law. Inverse variation means that as one variable increases, the other variable decreases by the same factor. The inverse square law states that the value of a quantity is inversely proportional to the square of the distance from the source.
Let's break down the problem step by step:
1. Determine the initial weight of Maria when she is on the surface of the Earth.
- We are given that Maria weighs 125 pounds on the surface of the Earth, which is 3960 miles from the center. This will be our initial weight, W1 = 125 pounds.
2. Calculate the weight of Maria at the top of Mount McKinley, which is 3.8 miles above the surface of the Earth.
- The new distance from the center of the Earth, including the height of Mount McKinley, is 3960 + 3.8 = 3963.8 miles.
- We can now set up the inverse variation equation using the inverse square law formula:
W1 / W2 = (d2^2) / (d1^2)
- Substituting the given values into the formula, we have:
125 / W2 = (3963.8^2) / (3960^2)
- Rearrange the equation to solve for W2:
W2 = 125 * (3960^2) / (3963.8^2)
3. Calculate Maria's weight at the top of Mount McKinley using the provided formula:
W2 = 125 * (3960^2) / (3963.8^2)
W2 ≈ 124.66 pounds
Therefore, Maria's weight at the top of Mount McKinley is approximately 124.66 pounds.