Question

Newton's Law of Gravitation can be used to show that if an object weighs w pounds on the surface of the earth, then its weight at distance x from the center of the earth is

W(x) = (wR^2/x^2 ) for x ? R , where R = 3,960 miles is the radius of the earth. At which altitude would an 130-lb person weigh 129.5 lbs? (Round your answer to two decimal places.)

answer in mi ?

Answer 1

An 130-lb person would weigh 129.5 lbs at an altitude of 3967.64 miles.

Explanation:

At which altitude would an 130-lb person weigh 129.5 lbs?

This is
`x` when
`w = 130, W(x) = 129.5, R = 3960`

`W(x) = (wr^(2))/(x^(2))`

`129.5 = (130*(3960)^(2))/(x^(2))`

`129.5x^(2) = 130*(3960)^(2)`

`129.5x^(2) = 2038608000`

`x^(2) = (2038608000)/(129.5)`

`x^(2) = 15742146.7181`

`x = √(15742146.7181)`

`x = 3967.64`

An 130-lb person would weigh 129.5 lbs at an altitude of 3967.64 miles.