Agirl delivering newspapers travels 2 blocks west, 5 blocks north, and then 6 blocks east. what is her resultant displacement? at ° counterclockwise from east.

Refer to the diagram shown below.

Define the displacement in the east as positive and displacement north as positive in y.

1st travel = (-2, 0)       2 blocks west
2nd travel = (0, 5)       5 blocks north
3rd travel =  (6, 0)       6 blocks east

Add x and y components for total displacement
Total x-displacement = -2 + 0 + 6 = 4
Total y-displacement = 0 + 5 + 0 = 5

The resultant displacement (from the Pythagorean theorem) is
d = √(4² + 5²) = 6.403 blocks
The angle that the resultant makes with the x-axis is
tan θ = 5/4 = 1.25
θ = tan⁻¹ 1.25 = 51.3°


6.4 blocks
51.3° counterclockwise from east

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