Answer to Question #242671 in Physics for Fadi

Question

 An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60 degrees north of west, then 50 steps due south. Assume his steps all have equal length. (a) Sketch, roughly to scale, the three vectors and their resultant. (b) Save the explorer from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut. (10)

Answer 1

(a) The sketch:

(b) The displacement to get back:

$$R_W=40\cos45°+80\cos60°=\\=68\text{ steps West},\\ R_S=40\sin45°+80\sin60°-50=\\=48\text{ steps North N}.$$