Chapter 1, Problem 33P

(III) Many sailboats are moored at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water’s edge, you can just see its duck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–12, where h = 1.5 m, estimate the radius R of the Earth.

FIGURE 1–12 Problem 33. You see a sailboat across a lake (not to scale). R is the radius of the Earth. You are a distance d = 4.4 km from the sailboat when you can see only its deck and not its side. Because of the curvature of the Earth, the water “bugles out” between you and the boat.