Question

The weight (in pounds) w =f(d) of an object varies inversely as the square of its distance (in thousands of miles) d from the center of Earth.A. An astronaut weighs 250 pounds at sea level (about 4 thousand miles from Earth's center). Find an equation of f b. How much would the astronaut weigh at 1 thousand miles above Earth's surface?

Answer 1

The astronaut will weigh 4,000 pounds

Explanation:

Weight varies inversely as square of distance from the center of the earth.

Mathematically, w * d^2 = K

where K is the constant of proportionality linking the weight and the distance from the center of the earth

Let’s calculate k first;

w = 250 pounds while d is 4,000

Thus k = 250 * 4,000^2 = 4,000,000,000

Now we need to know the weight of the astronaut at a distance of 1,000 miles above earth surface

To get this, we plug 1000 as the value for d while k still remains the same

From w * d^2 = k

w * 1000 * 1000 = 4,000,000,000

w = 4,000,000,000/1,000,000 = 4,000 pounds

The astronaut will weigh 4,000 pounds