Question

Amanda walks west 59 meters and north 55 meters. Calculate the magnitude and direction of her resultant displacement vector.

In your units box, provide the unit abbreviation and the direction in lowercase letters (for kilometers northwest, you would type "km nw" for blocks southeast you would type "blocks se" for meters northeast you would type "m ne").

Answer 1

Amanda's resultant displacement vector has a magnitude of approximately 80.66 meters and a direction of 43.2 degrees north of west.

Step-by-step explanation:

Amanda has walked a displacement of 59 meters west and 55 meters north. To calculate her resultant displacement vector, we can use the Pythagorean theorem because the two paths are at right angles to each other. The magnitude of the resultant displacement (R) would be the hypotenuse of a right-angled triangle with sides of 59 meters and 55 meters.

R = √(59² + 55²)
R = √(3481 + 3025)
R = √6506
R ≈ 80.66 meters

To find the direction, we can use the arctangent function to determine the angle of the displacement vector relative to the west direction.

Direction = arctan(opposite/adjacent)
Direction = arctan(55/59)
Direction ≈ 43.2° north of west

Therefore, the magnitude of Amanda's displacement is approximately 80.66 meters and the direction is 43.2° north of west.

The units in the format required would be: 80.66 m nw.