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. Save him 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.

Answer 1

place the hut at the origin (0,0). first segment is 40 steps northeast. no angle given, assume 45 deg. second segment is 80 steps 60 deg north of west, same thing as saying 60deg clockwise from negative x axis. third segment is 50 steps south, same as -90deg or 270 deg.

Answer 2

not sure if it should cross the y axis or not but it's not important

Answer 3

to break down his path into components, we need the points of x and y. x and y are calculated using i and j components.
segment 1:
(40cos45)i+(40sin45)j
segment 2:
(-80cos60)i+(80sin60)j negative i component because the direction is going left but still up so positive j component
segment 3:
(50cos90)i+(-50sin90)j i component will cancel since there's no x direction movement

Answer 4

add the segments component wise (add i components together, add j components together) which will give you his last position in (x,y) form.