Chapter 1: Problem 8
The two front legs of a tripod are each \(1.4 \mathrm{~m}\) long, with feet \(0.8 \mathrm{~m}\) apart. The third leg is \(1.5 \mathrm{~m}\) long, and its foot is \(1.5 \mathrm{~m}\) directly behind the midpoint of the line joining the other two. Find the height of the tripod, and the vectors representing the positions of its three feet relative to the top. (Hint: Choose a convenient origin and axes and write down the lengths of the legs in terms of the position vector of the top.) Given that the tripod carries a weight of mass \(2 \mathrm{~kg}\), find the forces in the legs, assuming they are purely compressional (i.e., along the direction of the leg) and that the legs themselves have negligible weight. (Take \(g=10 \mathrm{~ms}^{-2}\).)