Question

Now imagine that instead of walking along the path 1→2→3→4→1, ann walks 80 meters on a straight line 33∘ north of east starting at point 1. draw ann's path. represent ann's walk with a vector of length 80 meters.

Answer 1

Ann walks 80 meters with a direction of 33° north of east starting. This corresponds to a vector of
r = 80 m and θ = 33°
You draw this by making a coordinate system, two lines perpendicular to each other with the intersection as the origin. Next, locate the ray that would correspond to the direction of 33° north of east. On that ray and starting from the origin, measure 80 m or use a scale.

Answer 2

Anna's walk as a vector representation is
`80\cos 33^(\circ)\hat{i}+80 \sin33^(\circ)\hat{j}` and refer attachment.

Explanation:

Let the origin be the point 1 from where Ann start walking.

Ann walks 80 meters on a straight line 33° north of the east starting at point 1 as shown in figure below,

Resolving into the vectors, the vertical component will be 80Sin33° and Horizontal component will be 80Cos33° as shown in figure (2)

Ann walk as a vector representation is
`80\cos 33^(\circ)\hat{i}+80 \sin33^(\circ)\hat{j}`

Thus, Anna's walk as a vector representation is
`80\cos 33^(\circ)\hat{i}+80 \sin33^(\circ)\hat{j}`