A girl delivering newspapers covers her route by traveling 8.00 blocks west, 4.00 blocks north, and then 2.00 blocks east.
(a) What is her resultant displacement?
(b) What is the total distance she travels?
In the x-(east-)direction:
dx=-8+2=-6
In the y-(north-)direction:
dy=4
The resultant displacement is 6 blocks west and 4 blocks north.
Note: displacement is a vector, so it's the final and initial locations that count.
B. The total distance is 8+2+4=14 blocks.
Note: distance is not a vector, so we add up the absolute value of each leg.
kjknm
To find the girl's resultant displacement, we need to add up the individual displacements in each direction.
(a) To get the displacement in the east-west direction, we subtract the displacement traveled to the east from the displacement traveled to the west:
Resultant displacement in the east-west direction = 8.00 blocks west - 2.00 blocks east = 6.00 blocks west
To get the displacement in the north-south direction, we simply add up the displacement in the north direction:
Resultant displacement in the north-south direction = 4.00 blocks north
Thus, the girl's resultant displacement is 6.00 blocks west and 4.00 blocks north.
(b) To find the total distance she traveled, we need to sum up the distances traveled in each direction.
The distance traveled in the west direction is 8.00 blocks, in the north direction is 4.00 blocks, and in the east direction is 2.00 blocks.
Total distance traveled = Distance traveled in the west direction + Distance traveled in the north direction + Distance traveled in the east direction
Total distance traveled = 8.00 blocks + 4.00 blocks + 2.00 blocks = 14.00 blocks
Therefore, the girl traveled a total distance of 14.00 blocks.