One afternoon, a couple walks five-sixths of the way around a circular lake, the radius of which is 1.45 km. They start at the west side of the lake and head due south to begin with.
(a) What is the distance they travel?
(b) What are the magnitude and direction (relative to due east) of the couple's displacement?
distance=5/6 * 2PI *r
displacement: final point-initial point
Displacement= r@5/6 *360 - r@0
so in circular coordinates, displacement is r@300-r@0
Now in rectangular coordinates
displcement=r (sin60 N + cos60W)-r(sin0 N + cos0 W)
and you can work that out.posted by bobpursley