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°
Answer:
6.4 blocks
51.3° counterclockwise from east
