An explorer in antarctica leaves his shelter during a whiteout. he takes 40 steps northeast, next 80 steps at 60° north of west, and then 50 steps due south. assume all of his steps are equal in length. (a) sketch, roughly to scale, the three vectors and their resultant. (b) save the explorer from be- coming hopelessly lost by giving him the displacement, calculated by using the method of components, that will return him to his shelter. 1.73 .. while following a treasure map, you start at an old oak tree. you first walk 825 m directly south, then turn and walk 1.25 km at 30.0° west of north, and finally walk 1.00 km at 32.0° north of east, where you find the treasure: a biography of isaac newton! (a) to return to the old oak tree, in what direction should you head and how far will you walk? use components to solve this problem. (b) to see whether your calculation in part (a) is reason- able, compare it with a graphical solution drawn roughly to scale. 1.74 .. a fence post is 52.0 m from where you are standing, in a direction 37.0° north of east. a second fence post is due south from you. how far are you from the second post if the distance between the two posts is 68.0 m? 1.69 ..