Question

Edward runs 33.2 m north and then runs 62.4 m to the west. What is Edward's displacement in magnitude-direction notation? a. 95.6 m, north of west b. 95.6 m, west of north c. 95.6 m, south of east

Answer 1

The correct magnitude-direction notation for Edward's displacement is a. 70.72 m, north of west. None of the answer is correct.

Step-by-step explanation:

To determine Edward's displacement in magnitude-direction notation, we can use the Pythagorean theorem and trigonometric functions.

1. First, we calculate the magnitude of Edward's displacement using the Pythagorean theorem:

Displacement magnitude = √(33.2^2 + 62.4^2)

Displacement magnitude = √(1102.24 + 3897.76)

Displacement magnitude = √5000

Displacement magnitude ≈ 70.71 m

2. Next, we determine the direction of the displacement. We can use the tangent function to find the angle between the displacement vector and the north direction.

tan(θ) = opposite/adjacent

tan(θ) = 33.2/62.4

θ = arctan(33.2/62.4)

θ ≈ 27.15°

3. Finally, we express the displacement in magnitude-direction notation, where the direction is given as an angle measured counterclockwise from the positive x-axis (east) and the magnitude is the length of the displacement vector.

Therefore, Edward's displacement in magnitude-direction notation is approximately 70.71 m at an angle of 27.15° west of north.