direct variation question

Question

if a woman weighs 120 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 4.6 miles above sea level

Answer 1

Her weight is inversely proportional to the square of her distance from the center of the earth.

 

You can express this as W = k/D²

 

W is her weight

D is her distance from the center of the earth

k is the "constant of proportionality"

 

Initially D is 3960.  When she is at the top of the mountain, it is 3964.6.  The ratio between these two heights is 3964.6 / 3960.  The square of this ratio is (3964.6 / 3960)².  So when her distance increases, her weight will DECREASE by the squared ratio.

 

So to find her weight at the top of the mountain, divide 120 by (3964.6 / 3960)².  That gives 119.72 pounds.