Question

Starting from point A, Peter walks 10 m due west to point B. From point B, he walks 10 m, 36°NE to point C. He then walks 10 m, 72° SW to point D. Find the magnitude of the displacement from A to D

Answer 1

By adding up the west and east components separately, we can calculate the total displacement. The magnitude of the displacement from A to D is 18.13 m.

Step-by-step explanation:

To find the magnitude of the displacement from A to D, we can break down the displacement into its north and west components. From point A to point D, Peter walks 10 m due west, which contributes to the west component of the displacement. Next, he walks 10 m, 36°NE, which can be broken down into a north and west component. Finally, he walks 10 m, 72° SW, which contributes to the east component of the displacement.

By adding up the west and east components separately, we can calculate the total displacement.

West component: 10 m + 10 m * cos(36°) = 10 m + 10 m * 0.809 = 10 m + 8.09 m = 18.09 m

East component: 10 m * cos(72°) = 10 m * 0.309 = 3.09 m

To find the magnitude of the displacement, we can apply the Pythagorean theorem:

Magnitude of displacement: √((18.09 m)2 + (3.09 m)2) = √(327.5481 + 9.5481) = 18.13 m