A girl delivering newspapers covers her route by traveling 2.50 blocks west, 3.50 blocks north, and then 5.50 blocks east.
To find the total displacement of the girl delivering newspapers, we need to calculate the net distance and direction of her route.
Step 1: Calculate the total displacement in the x-direction (east/west).
The girl travels 2.50 blocks west and then 5.50 blocks east.
Net displacement in the x-direction = 5.50 blocks east - 2.50 blocks west = 3.00 blocks east.
Step 2: Calculate the total displacement in the y-direction (north/south).
The girl travels 3.50 blocks north.
Net displacement in the y-direction = 3.50 blocks north.
Step 3: Calculate the total displacement magnitude and direction.
Using the Pythagorean theorem, we can calculate the displacement magnitude.
Displacement magnitude = sqrt((3.00)^2 + (3.50)^2) = sqrt(9 + 12.25) = sqrt(21.25) ≈ 4.61 blocks.
To determine the direction, we can use trigonometry.
Displacement angle = atan(3.50 / 3.00) ≈ 48.37 degrees north of east.
Therefore, the girl's route results in a displacement of approximately 4.61 blocks, 48.37 degrees north of east.
To find the total distance covered by the girl delivering newspapers, we need to calculate the sum of the individual distances traveled in each direction.
1. Distance traveled west: The girl traveled 2.50 blocks west.
2. Distance traveled north: The girl traveled 3.50 blocks north.
3. Distance traveled east: The girl traveled 5.50 blocks east.
To find the total distance, we can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the total distance traveled will be the hypotenuse of a right triangle formed by the distances traveled west and north.
Using the Pythagorean theorem:
Total distance = √(Distance west² + Distance north²)
Substituting the given values:
Total distance = √(2.50² + 3.50²)
Calculating the squares:
Total distance = √(6.25 + 12.25)
Adding the two squares:
Total distance = √18.50
Taking the square root:
Total distance ≈ 4.30 blocks
Therefore, the girl covers a total distance of approximately 4.30 blocks.