8. 35. 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 = 3,960 miles is the radius of the earth.
Show that the weight lost at altitude h miles above the earth’s surface is approximately ΔW ≈ −(0.0005w)h.
Hint: 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.

9. 39. A player located 18.1 ft from the basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle θ = 34° and initial velocity v = 25 ft/s.)
(a) Show that Δs ≈ 0.255Δθ ft for a small change of Δθ.
(b) Is it likely that the shot would have been successful if the angle
had been off by 2°?