Question

problem 1
you walk west 220m and then north 150m.
a) what is the magnitude of your displacement vector?
b) what is the direction of your displacement vector?

Explanation:

Step1: Displacement components (west, north)

West: 220m, North: 150m (perpendicular)

Step2: Apply Pythagorean theorem

Magnitude \( \sqrt{220^2 + 150^2} \)

Step3: Calculate magnitude value

\( \sqrt{48400 + 22500} = \sqrt{70900} \approx 266m \)

Step4: Direction angle (north of west)

\( \tan\theta = \frac{150}{220} \approx 0.6818 \)

Step5: Compute angle

\( \theta = \arctan(0.6818) \approx 34^\circ \)

Answer:

a) 266 m
b) Approximately 34 degrees north of west