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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.

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barnuts

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

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