A girl delivering newspapers travels 3 blocks west, 6 blocks north, then 5 blocks east. What is the magnitude of her resultant displacement? .

Question

Find the direction (measured from due east, with counterclockwise positive) of her displacement. What is the total distance she travels? Answer in units of blocks

Answer 1

To find the direction of a resultant vector, you would use the equation:

θ = arctan(y/x) = tan^-1(y/x)

Therefore, we need to know the displacement north/south and displacement east/west. Since all of the movements are already in a cardinal direction, we can simply add the vectors. We find that:

y = +6 blocks

x = -3 + 5 = +2 blocks

We subtract the three since it is west. In standard systems, West and South are typically negative while East and North are positive. Once we have that information, we can plug it into our equation above to get:

θ = arctan(6/2) = tan^-1(6/2) =71.6 degrees N of E

Distance is the actual amount an object (in this case the girl) travels. It should not be confused with displacement, which is the straight line distance between start and end points. To calculate distance, you simply add up all the individual movements:

dist = 3 + 6 + 5 = 14 Blocks