Question

The weight of an object varies inversely as the square of the distance from the center of the earth. At sea level (6400 km from the center of the earth), an astronaut weighs 100 lb. How far above the earth must the astronaut? be in order to weigh 64 lb

Answer 1

Answer:

The astronaut must be at 1600 km from the earth to weight 64lb

Step-by-step explanation:

As the weight of an object varies inversely as the square of the distance from the center of the earth, that means that:

weight = k / distance² (1)

Where k is proportionality constant

Replacing:

100 lb = k/(6400km)²

100lb × 6400km² = k = 4,096x10⁹ lbkm²

Now, using (1):

64 lb = 4,096x10⁹ lbkm² / x²

x² = 4,096x10⁹ lbkm² / 64lb

x² = 6,4x10⁷ km²

x = √6,4x10⁷ km²

x = 8000 km

Distance from the center of the earth is 8000 km. Distance from the earth (At sea level):

8000km - 6400km = 1600km

I hope it helps!