A delivery truck travels 21 blocks north, 17 blocks east, and 27 blocks south.
What is its final displacement from the origin (direction)?
went 21 - 27 = -6 blocks north
went 17 east
magnitude = sqrt (17^2 + 6^2)
tangent of angle south of east = 6/17
angle clockwise from north (compass bearing from origin) = 90 + tan^-1(6/17)
To calculate the final displacement, we need to find the net displacement in both the north-south (vertical) and east-west (horizontal) directions.
1. First, let's calculate the north-south displacement:
The truck travels 21 blocks north and 27 blocks south. To find the net displacement, we subtract the southward distance from the northward distance: 21 - 27 = -6 blocks.
The negative sign indicates that the truck traveled more south than north, resulting in a displacement in the southward direction.
2. Now, let's calculate the east-west displacement:
The truck travels 17 blocks east. Since there is no westward distance, we simply take the distance as positive: 17 blocks.
The east-west displacement is positive, indicating movement in the eastward direction.
3. Finally, we can determine the final displacement:
We combine the vertical and horizontal displacements to find the final displacement.
The final displacement consists of both magnitude and direction. To find the magnitude, we can use the Pythagorean theorem (a^2 + b^2 = c^2), where a and b represent the vertical and horizontal displacements, and c represents the magnitude of the final displacement.
Using the formula: c = √((-6)^2 + 17^2) = √(36 + 289) = √325 ≈ 18.03 blocks.
The magnitude of the final displacement is approximately 18.03 blocks.
As for the direction, we can use trigonometry to determine the angle between the final displacement vector and the positive x-axis (east).
The angle, θ, can be found using the inverse tangent (arctan) function: θ = arctan(vertical displacement / horizontal displacement).
θ = arctan((-6) / 17) ≈ -19.98 degrees.
Since the displacement is in the fourth quadrant, we need to add 180 degrees to obtain the positive measurement: θ ≈ 160.02 degrees.
Therefore, the final displacement from the origin is approximately 18.03 blocks in the southeast direction (at an angle of approximately 160.02 degrees with respect to the positive x-axis).
To calculate the final displacement from the origin, we need to find the net distance and direction traveled by the delivery truck.
First, let's analyze the north and south movements. The truck traveled 21 blocks north and then 27 blocks south. To find the net distance of these movements, we subtract the south movement from the north movement: 21 - 27 = -6. This means the net north-south displacement is 6 blocks south.
Next, let's analyze the east movement. The truck traveled 17 blocks east. This movement does not affect the net north-south displacement.
Therefore, the final displacement from the origin is 6 blocks south.