Newton’s Law of Gravitation shows that if a person weighs w pounds on the surface of the earth, then his or her weight at distance x from the center of the earth is

where R = 3960 miles is the radius of the earth (Figure 10).

(a) Show that the weight lost at altitude h miles above the earth’s surface is approximately ΔW ≈ −(0.0005w)h. Use the Linear Approximation with dx = h.
(b) Estimate the weight lost by a 200-lb football player flying in a jet at an altitude of 7 miles.

Transcribed Image Text:

W(x) = WR² x2 (for x ≥ R)