A delivery truck travels 20 blocks south, 24 blocks west and 25 blocks north. What is its final displacement from the origin? Assume the blocks are equal length.

Need magnitude of blocks, and direction(counterclockwise from east is positive)

add them.

20S+24W+25N=-20N+24W+25N=5N+24W

I will be happy to critique your work from here.

4.3 degrees

To calculate the final displacement of the delivery truck from the origin, we need to find the vector sum of its individual displacements in each direction (north and west).

1. Start by assigning a coordinate system with the positive x-axis pointing east and the positive y-axis pointing north.
2. First, let's consider the north-south direction. The truck travels 20 blocks south and then 25 blocks north. Since these displacements are in opposite directions, we can subtract the south displacement from the north displacement to find the net displacement in the north-south direction.

Net displacement in the north-south direction = 25 blocks north - 20 blocks south = 5 blocks north.

3. Next, let's consider the west-east direction. The truck travels 24 blocks west. Since there is no eastward displacement mentioned, we assume it to be zero.

Net displacement in the west-east direction = 24 blocks west - 0 blocks east = 24 blocks west.

4. Now, we have the net displacements in both the north-south and west-east directions. To find the final displacement, we can calculate the magnitude and direction of the resultant vector using the Pythagorean theorem and trigonometry.

Magnitude of displacement = √(net displacement in the north-south direction)^2 + (net displacement in the west-east direction)^2
= √(5^2 + 24^2)
= √(25 + 576)
= √601
≈ 24.5 blocks.

Direction (counterclockwise from east as positive):
We can use the tangent of the angle to find the direction.

tan(angle) = (net displacement in the north-south direction) / (net displacement in the west-east direction)
tan(angle) = 5 / 24
angle = arctan(5 / 24)
angle ≈ 11.5 degrees.

Since the truck travels 24 blocks west, the final displacement is 24.5 blocks at an angle of approximately 11.5 degrees counterclockwise from the east direction.