A girl delivering newspapers covers her route by traveling 6.00 blocks west, 4.00 blocks north, and then 4.00 blocks east.
(a) What is her resultant displacement?
(b) What is the total distance she travels?
displacement =sqrt[4² +(6-4)²]=4.24 m,
distance = 6+4+4 =14 m
Duff
To find the resultant displacement of the girl, we need to calculate the net displacement from her starting point to her ending point. We can do this by considering the horizontal (east-west) and vertical (north-south) components separately.
(a) Horizontal displacement:
The girl travels 6.00 blocks west and then 4.00 blocks east. These two displacements cancel each other out since she returns to her starting point. Therefore, her horizontal displacement is 0 blocks.
Vertical displacement:
The girl travels 4.00 blocks north. This is her final displacement in the north direction.
Therefore, the resultant displacement can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (resultant displacement) is equal to the sum of the squares of the other two sides (horizontal and vertical displacements).
Resultant displacement^2 = Horizontal displacement^2 + Vertical displacement^2
Resultant displacement^2 = 0^2 + 4.00^2
Resultant displacement^2 = 0 + 16.00
Resultant displacement^2 = 16.00
Resultant displacement = √16.00
Resultant displacement = 4.00 blocks
So, her resultant displacement is 4.00 blocks north.
(b) To find the total distance she travels, we need to consider the length of each leg of her route. The total distance is the sum of these lengths.
Distance traveled west = 6.00 blocks
Distance traveled north = 4.00 blocks
Distance traveled east = 4.00 blocks
Total distance = Distance traveled west + Distance traveled north + Distance traveled east
Total distance = 6.00 + 4.00 + 4.00
Total distance = 14.00 blocks
Therefore, the total distance she travels is 14.00 blocks.