Problema Solution
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 136 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, 3.8 miles above sea level?
Answer provided by our tutors
let
w = the weight
d = the distance from the center of the Earth
w = k/(d^2)
we know w = 136 lbs for d = 3960 that is
136 = k/(3960^2)
k = 136*(3960^2)
at the top of a mountain d = 3960 + 3.8 = 3963.8 lbs
w = k/(3963.8^2)
plug k = 136*(3960^2) into the last equation
w = (136*(3960^2))/(3963.8^2)
w = 135.7385 lbs
the weight on the top of the mountain is 135.7385 lbs.