Question

While playing Pokemon Go on campus, a student walked the following:
67m North
32m East
35m SouthWest (direction halfway between South and West)
98m South
22m NorthWest (direction halfway between North and West)
53m West
48m North
What is the magnitude of the student's final displacement in m?
(Hint: Add up all N/S-components and E/W-components separately, then recombine)

Answer 1

Displacements within x axis (east + / west -):

$\Delta x = (32 - 35\cos\frac{\pi}{4} - 22\cos\frac{\pi}{4} - 53) \text{ m} \approx -61.305 \text{ m}.$

Displacements within y axis (north + / south -):

$\Delta y = (67 - 35\sin\frac{\pi}{4} - 98 + 22\sin\frac{\pi}{4} + 48) \text{ m} \approx 7.808 \text{ m}.$

Combined displacement:

$\Delta s = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(-61.305)^2 + (7.808)^2} \text{ m} \approx 61.800 \text{ m}.$