Determine the vector sum of the displacements Δd1 = 2.4 m [32° S of W]; Δd2 = 1.6 m [S]; and Δd3 = 4.9 m [27° S of E].

3.44 metres

Explanation:

To determine the vector sum of the displacements Δd1 = 2.4 m [32° S of W]; Δd2 = 1.6 m [S]; and Δd3 = 4.9 m [27° S of E], resolve the given parameters into x - component and y - component.

Resolving into x - component

- 2.4cos32 + 4.9cos27 = 2.3306

Resolving into y - component

- 2.4sin32 - 4.9sin27 - 1.6 = - 2.553

The vector sum of the displacement will be

Sqrt( 2.3^2 + 2.6^2) =

Sqrt ( 11.81)

3.44 m

Therefore, the vector sum of the displacements is 3.44 metres

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