Ahiker walks 4 km north and then 5 km northeast. draw displacement vectors representing the hiker's trip and draw a vector that represent

R = 8.33 km

,  θ = 64.9⁰

Explanation:

For this exercise, we can see the attachment.

The resulting displacement can also be found analytically, for this we find the displacement on each axis

Let's start with decompile [put the second displacement (L)

                sin 45 = y2 / L

                cos45 = x2 / L

               y2 = L sin 45

               x2 = L cos45

               y2 = 5 sin 45 = 3.54 km

               x2 = 5 cos 45 = 3.54 km

The components of the displacements are

                   X = x2

                   X = 3.54 km

                   Y = y1 + y2

                   Y = 4 + 3.54

                   Y = 7.54 km

In module this displacement is

                  R = √ X² + Y²

                  R = √ 3.54² + 7.54²

                  R = 8.33 km

We look for the angle with trigonometry

                 tan θ = Y / X

                 θ = tan⁻¹ Y / X

                 θ = tan⁻¹ 7.54 / 3.54

                 θ = 64.9

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