Ruth sets out to visit her friend Ward, who lives 60 mi north and 100 mi east of

Question

Ruth sets out to visit her friend Ward, who lives 60 mi north and 100 mi east of her. She starts by driving east, but after 30 mi she comes to a detour that takes her 15 mi south before going east again. She then drives east for 8 mi and runs out of gas, so Ward flies there in his small plane to get her.

What is Ward's displacement vector? Give your answer in component form, using a coordinate system in which the y-axis points north.

What is the magnitude of Ward's displacement vector?

Whatt is the direction of Ward's displacement vector, measured clockwise from the negative y axis?

Explanation / Answer

Taking y(j) as east and x(i) as north , and Ruth's location as origin,

initial locations:

0i + 0j for Ruth

100i + 60j for Ward

final locations:

0+30+8 i + 0-15 j or 38i - 15j for Ruth

so Ward's displacement vector = 38-100 i + -15-60 j = -62i - 75j

magnitude of Ward's displacement vector = ((-62)2+(-75)2)1/2 = 97.3 units

since both i and j are -ve, it is in 3rd quadrant

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