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

Answer:

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

Step-by-step explanation:

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

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

$W(x) = \frac{wr^{2}}{x^{2}}$

$129.5 = \frac{130*(3960)^{2}}{x^{2}}$

$129.5x^{2} = 130*(3960)^{2}$

$129.5x^{2} = 2038608000$

$x^{2} = \frac{2038608000}{129.5}$

$x^{2} = 15742146.7181$

$x = \sqrt{15742146.7181}$

$x = 3967.64$

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