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# Problem: Ruth sets out to visit her friend Ward, who lives 40 mi north and 100 mi east of her. She starts by driving east, but after 50 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.(a) What is Wards displacement vector? Give your answer in component form, using a coordinate system in which the y-axis points north.(b) What is the magnitude of Wards displacement vector?(c) What is the direction of Wards displacement vector, measured clockwise from the negative y axis?

###### FREE Expert Solution

In this problem, we are dealing with plotting vectors graphically. After plotting we'll determine the final position and displacement.

North points in the y-axis. East points in the x-axis. South points  All distances are in miles.

Wards initial position is (x,y) = (100,40)

Ruth's initial position is located at the origin (x,y) = (0,0)

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###### Problem Details

Ruth sets out to visit her friend Ward, who lives 40 mi north and 100 mi east of her. She starts by driving east, but after 50 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.

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

(b) What is the magnitude of Wards displacement vector?

(c) What is the direction of Wards displacement vector, measured clockwise from the negative y axis?