A bear, awakening from winter hibernation, staggers directly northeast for 15 m and then due east for 15 m. Show each displacement graphically and graphically determine the single displacement that will take the bear back to her cave to continue her hibernation.

The total displacement east is:

15 cos (45) + 15

= 25.607 m

The total displacement north is:

15 sin (45)

= 10.607 m

The magnitude of the total displacement is:

sqrt (25.607^2 + 10.607^2)

= 27.717 m = 27.7 m

Its direction is N x E where:

tan (x) = 25.607 / 10.607

x = 67.5 deg

The return displacement is therefore of the same magnitude but in the opposite direction.

Displacement 27.7 m, direction S 67.5 deg W