Question

The weight of a body above sea level varies inversely with the square of the distance from the center of Earth. If a woman weighs 123 pounds when she is at sea​ level, 3960 miles from the center of​ Earth, how much will she weigh when she is at the top of a​ mountain, 3.2 miles above sea​ level?

Answer 1

Her weight is approximately 122.8lb

Explanation:

Given

Inverse proportion;

Weight = 123lb when distance = 3960 miles from center of earth

Required

Calculate the weight when distance is 3.2 miles above sea level

Let weight be represented by W and distance by D

From the question, we understand that;

Weight is inversely proportional to square of distance;

Mathematically; this is

`W \alpha \ (1)/(D^2)`

Convert proportion to equation

`W = (k)/(D^2)`

Where k is the constant of proportionality

When W = 123; D = 3960.

This implies that

`123 = (k)/(3960^2)`

Make k the subject of formula

`k = 123 * 3960^2`

`k = 1928836800`

Calculating her weight when she's at the top of mountain, 3.2 miles above sea level

First, her distance from center of earth has to be calculated

Distance = Previous distance + 3.2

Distance = 3960 + 3.2

Distance = 3963.2

Now, her weight can be calculated using
`W = (k)/(D^2)`

Substitute for k and D

`W = (1928836800)/(3963.2^2)`

`W = (1928836800)/(15706954.24)`

`W = 122.801452817`

`W = 122.8\ (Approximated)`