Question

One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 1.03 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 is the magnitude of the couple’s displacement? (c) What is the direction (relative to due east) of the couple’s displacement?

Answer 1

Distance=0.75• 2•π•R=0.75•2•π•1.03=4.85 km.
Displacement is =2√R=2√1.03=2.03 km
direction 45ºrestectively - x-axis direction
or 135º respectively +x-direction

Answer 2

Displacement is 1.03^2*1.03^2=c^2 the third side is your displacement