Application problem

Question

If Amy weighs 120 lbs at sea level, how much will she weigh on Pike's Peak, which is 14,110 ft above sea lvl?

If an object weighs m pounds at sea level. then its weight W (in lbs) at height of h miles above sea level is given approximately by the equation

W(h) = m(4000/4000+h)^2 

a) answered, need help with b!

b)At what height will Amy weigh 119.95 lbs

Answer 1

Hi Natalie H.,

Just plug in values and solve through.

119.95 = 120(4000/(4000+h))^2

120/119.95 = ((4000+h)/4000)^2

1.00041684035 = (1 + (h/4000))^2 . Take sqrt each side:

1.00020839846 = 1 + h/4000

0.00020839846 = h/4000

h=0.83359384045 or ~4401 ft above sea level.

Of course, the given equation is an approximation which does include corrections for irregularities of composition of the Earth, "centrifugal" force, and so on. see: (search for) dn24068-gravity-map .

-- Cheers, -- Mr. d.