Final answer:
To find the new weight of a person 850 miles above Earth's surface, you calculate the total distance from Earth's center and apply the inverse square law. The person's new weight is approximately 121.34 lbs, which is answer A.
Step-by-step explanation:
The weight of a person above the surface of the earth varies inversely with the square of the distance from the center of the earth. This concept is based on Newton's Law of Universal Gravitation, which is fundamental in understanding gravitational forces. To calculate the new weight of a person 850 miles above the Earth's surface, we first need to determine the total distance from the center of the Earth, which will be the sum of the Earth's radius (3900 miles) and the altitude above the surface (850 miles).
After calculating this total distance, we apply the inverse square law to determine the factor by which the person's weight will change. The weight at the new altitude is given by the formula:
W2 = W1 × (R1 / R2)²
Where W1 is the initial weight, R1 is the Earth's radius, W2 is the weight at the new altitude, and R2 is the total distance from the Earth's center at the new altitude. When we plug in the numbers:
W2 = 180 lbs × (3900 miles / (3900 miles + 850 miles))²
After performing the calculation, the new weight (to the nearest hundredth of a pound) is approximately 121.34 lbs. Hence, the correct answer is A. 121.34 lb.