Final answer:
Using the inverse square law for gravity, we calculate that a woman weighing 120 pounds at sea level would weigh approximately 119.63 pounds at the top of a mountain that is 3.5 miles above sea level.
Step-by-step explanation:
The weight of a body above sea level does indeed vary inversely with the square of the distance from the center of Earth. Since weight is directly proportional to the force of gravity, and gravity decreases with the square of the distance from the source (which in this case is the center of Earth), we can use the inverse square law to determine the woman's weight at the top of the mountain.
The formula for weight variation with distance is given by:
W1/W2 = (d2/d1)^2
Where W1 is the original weight at sea level, W2 is the weight at the new altitude, d1 is the original distance from the center of the Earth, and d2 is the new distance from the center of the Earth.
In this case, the woman weighs 120 pounds at sea level, which is 3060 miles from the center of Earth. The mountain is 3.5 miles above sea level, making the new distance 3060 + 3.5 = 3063.5 miles. Plugging in the values, we get:
120/W2 = (3063.5/3060)^2
Solving for W2, the weight of the woman at the top of the mountain, we find:
W2 = 120 / (3063.5/3060)^2
W2 ≈ 119.63 pounds
The woman will weigh approximately 119.63 pounds at the top of the mountain. Since the problem requests an integer or a decimal rounded to two decimal places, the answer is 119.63 pounds.