Question

Repeat the problem two problems prior, but for the second leg, you walk 20.0 m in a direction 40.0º. (b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0º east of south (which is equivalent to subtracting A from B —that is, to finding R′′=B-A=-R′). Show that this is the case.

What is the magnitude of the displacement for the second leg when walking 20.0 m in a direction 40.0º?
1. 20.0 m
2. 15.3 m
3. 16.2 m
4. 22.7 m

Answer 1

The magnitude of displacement for the second leg is simply the total distance walked, which remains at 20.0 m, since it is a straight-line walk in a specified direction.

Step-by-step explanation:

The magnitude of the displacement for the second leg when walking 20.0 m in a direction 40.0° is a straightforward calculation based on trigonometry. Since the question involves a displacement vector, we need to consider the horizontal and vertical components separately. However, the magnitude of a displacement is the straight-line distance from start to end, not the sum of these components.

To find this displacement, we use the cosine and sine functions for the respective horizontal and vertical components, but since we are only asked for the magnitude of the displacement vector itself and it is a straight walk in one direction, the magnitude is just the length of the walk. Therefore, the magnitude of displacement is the total distance walked, which is 20.0 m.