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.

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°?