A girl delivering newspapers travels 2 blocks west, 1 blocks north, and then 7 blocks east.
(a) What is her resultant displacement?
_________ blocks at __________
2 ° counterclockwise from east.
(b) What is the total distance she travels?
__________ blocks
To find the girl's resultant displacement, we need to calculate the horizontal and vertical components of her displacement separately.
(a) Horizontal Component:
The girl travels 2 blocks west and then 7 blocks east. The displacement in the horizontal direction is the difference between the two distances. Since she moves west first, we consider it negative:
Horizontal displacement = -2 blocks + 7 blocks = 5 blocks east
Vertical Component:
The girl travels 1 block north. There are no displacements in the south direction, so we consider it positive.
Vertical displacement = 1 block north
Now, we can find the resultant displacement 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 = √(horizontal displacement)^2 + (vertical displacement)^2
Resultant displacement = √(5 blocks east)^2 + (1 block north)^2
Resultant displacement = √(25 blocks) + (1 block)
Resultant displacement = √26 blocks
Therefore, the girl's resultant displacement is √26 blocks at an angle of 2° counterclockwise from east.
(b) To find the total distance the girl travels, we need to sum up the distances traveled in each direction.
Distance traveled = |2 blocks west| + |1 block north| + |7 blocks east|
Distance traveled = 2 blocks + 1 block + 7 blocks
Distance traveled = 10 blocks
Therefore, the girl travels a total distance of 10 blocks.